Advances in Mathematics, ISSN 0001-8708, 07/2019, Volume 350, pp. 256 - 303

...) and their embedded cohomology jump loci, around the trivial representation 1. When the space M admits a finite family of maps, uniformly modeled...

Flat connection | Filtered differential graded algebra | Cohomology jump loci | Representation variety | Artinian local ring | Deformation theory | RESONANCE VARIETIES | SPACES | CONNECTIONS | MATHEMATICS | FUNDAMENTAL-GROUPS | REPRESENTATION VARIETIES | MULTINETS | GEOMETRY | Analysis | Algebra

Flat connection | Filtered differential graded algebra | Cohomology jump loci | Representation variety | Artinian local ring | Deformation theory | RESONANCE VARIETIES | SPACES | CONNECTIONS | MATHEMATICS | FUNDAMENTAL-GROUPS | REPRESENTATION VARIETIES | MULTINETS | GEOMETRY | Analysis | Algebra

Journal Article

Compositio mathematica, ISSN 0010-437X, 08/2015, Volume 151, Issue 8, pp. 1499 - 1528

.... The results obtained describe the analytic germs of the cohomology jump loci inside the corresponding moduli space, extending previous results of Goldman–Millson, Green...

cohomology jump locus | deformation theory | differential graded Lie algebra | local system | MATHEMATICS | MODULI SPACE | Algebra | Deformation | Mathematical analysis | Lie groups | Representations | Vectors (mathematics) | Loci | Bundles | Mathematics - Algebraic Geometry

cohomology jump locus | deformation theory | differential graded Lie algebra | local system | MATHEMATICS | MODULI SPACE | Algebra | Deformation | Mathematical analysis | Lie groups | Representations | Vectors (mathematics) | Loci | Bundles | Mathematics - Algebraic Geometry

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2018, Volume 70, Issue 2, pp. 695 - 709

.... We prove a general result that leads, in both cases, to the complete description of the analytic germs at the origin, for the corresponding embedded rank 2 jump loci.

Analytic germ | Solvmanifold | Characteristic variety | Lie algebra | Representation variety | Resonance variety | MATHEMATICS | resonance variety | solvmanifold | representation variety | COHOMOLOGY | MODELS | characteristic variety | VARIETIES | SYSTEMS | analytic germ | GEOMETRY

Analytic germ | Solvmanifold | Characteristic variety | Lie algebra | Representation variety | Resonance variety | MATHEMATICS | resonance variety | solvmanifold | representation variety | COHOMOLOGY | MODELS | characteristic variety | VARIETIES | SYSTEMS | analytic germ | GEOMETRY

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2014, Volume 16, Issue 4, pp. 1350025 - 1-1350025-47

For a space, we investigate its CJL (cohomology jump loci), sitting inside varieties of representations of the fundamental group...

analytic local ring | quasi-projective manifold | nilmanifold | Artinian ring | arrangement | cohomology support loci | covariant derivative | formal space | Representation variety | flat connection | monodromy | Malcev completion | minimal model | KAHLER-MANIFOLDS | MATHEMATICS, APPLIED | NILPOTENT GROUPS | DEFORMATION-THEORY | HOMOTOPY THEORY | COMPACT KAHLER | LIE-ALGEBRAS | MATHEMATICS | FORMALITY PROPERTIES | FUNDAMENTAL-GROUPS | COEFFICIENTS | Origins | Algebra | Mathematical analysis | Spectra | Representations | Topology | Loci | Joints

analytic local ring | quasi-projective manifold | nilmanifold | Artinian ring | arrangement | cohomology support loci | covariant derivative | formal space | Representation variety | flat connection | monodromy | Malcev completion | minimal model | KAHLER-MANIFOLDS | MATHEMATICS, APPLIED | NILPOTENT GROUPS | DEFORMATION-THEORY | HOMOTOPY THEORY | COMPACT KAHLER | LIE-ALGEBRAS | MATHEMATICS | FORMALITY PROPERTIES | FUNDAMENTAL-GROUPS | COEFFICIENTS | Origins | Algebra | Mathematical analysis | Spectra | Representations | Topology | Loci | Joints

Journal Article

5.
Full Text
RANK TWO TOPOLOGICAL AND INFINITESIMAL EMBEDDED JUMP LOCI OF QUASI-PROJECTIVE MANIFOLDS

Journal of the Institute of Mathematics of Jussieu, ISSN 1475-3030, 2018, Volume 19, Issue 2, pp. 1 - 35

We study the germs at the origin of -representation varieties and the degree 1 cohomology jump loci of fundamental groups of quasi-projective manifolds. Using the Morgan...

admissible map | representation variety | differential graded algebra model | quasi-projective manifold | holonomy Lie algebra | semisimple Lie algebra | cohomology jump loci | analytic germ | Deligne weight filtration | variety of flat connections | REPRESENTATIONS | VARIETIES | MATHEMATICS | COHOMOLOGY | GEOMETRY | Homology | Inclusions | Loci | Subgroups | Linear algebra

admissible map | representation variety | differential graded algebra model | quasi-projective manifold | holonomy Lie algebra | semisimple Lie algebra | cohomology jump loci | analytic germ | Deligne weight filtration | variety of flat connections | REPRESENTATIONS | VARIETIES | MATHEMATICS | COHOMOLOGY | GEOMETRY | Homology | Inclusions | Loci | Subgroups | Linear algebra

Journal Article

Central European Journal of Mathematics, ISSN 1895-1074, 9/2014, Volume 12, Issue 9, pp. 1285 - 1304

...Cent. Eur. J. Math. · 12(9) · 2014 · 1285-1304 DOI: 10.2478/s11533-014-0413-2 Central European Journal of Mathematics Novikov homology , jump loci and Massey...

Massey products | 58E05 | Topological Groups, Lie Groups | 53B35 | Probability Theory and Stochastic Processes | Kähler manifolds | Mathematics | Spectral sequence | Geometry | Algebra | 14F40 | 55N25 | Cohomology with twisted coefficients | Mathematics, general | Number Theory | Novikov homology | KAHLER-MANIFOLDS | MATHEMATICS | Kahler manifolds | SOLVMANIFOLDS | CLOSED 1-FORMS

Massey products | 58E05 | Topological Groups, Lie Groups | 53B35 | Probability Theory and Stochastic Processes | Kähler manifolds | Mathematics | Spectral sequence | Geometry | Algebra | 14F40 | 55N25 | Cohomology with twisted coefficients | Mathematics, general | Number Theory | Novikov homology | KAHLER-MANIFOLDS | MATHEMATICS | Kahler manifolds | SOLVMANIFOLDS | CLOSED 1-FORMS

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2016, Volume 2016, Issue 13, pp. 3849 - 3855

Cohomology support loci of rank one local systems of a smooth quasi-projective complex algebraic variety are finite unions of torsion-translated complex subtori of the character variety of the fundamental group...

MATHEMATICS | COHOMOLOGY JUMP LOCI

MATHEMATICS | COHOMOLOGY JUMP LOCI

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 306, pp. 905 - 928

We prove that the cohomology jump loci of rank one local systems on the complement in a small ball of a germ of a complex analytic set are finite unions of torsion translates of subtori...

Local systems | Riemann–Hilbert correspondence | Cohomology | Jump loci | MATHEMATICS | D-MODULE | VANISHING PROXIMITY | EQUATIONS | MANIFOLDS | Riemann-Hilbert correspondence | COHOMOLOGY JUMP LOCI

Local systems | Riemann–Hilbert correspondence | Cohomology | Jump loci | MATHEMATICS | D-MODULE | VANISHING PROXIMITY | EQUATIONS | MANIFOLDS | Riemann-Hilbert correspondence | COHOMOLOGY JUMP LOCI

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2019, Volume 354, p. 106754

.... As a first application, we show that for complex algebraic varieties with no weight-zero 1-cohomology classes, the components of the cohomology jump loci of rank one local systems containing the constant sheaf are tori...

Links | Milnor fibers | Weight filtration | Deformation theory | Fundamental group | L-infinity algebras and modules | TOPOLOGY | MATHEMATICS | SYSTEMS | HOMOTOPY | COHOMOLOGY JUMP LOCI

Links | Milnor fibers | Weight filtration | Deformation theory | Fundamental group | L-infinity algebras and modules | TOPOLOGY | MATHEMATICS | SYSTEMS | HOMOTOPY | COHOMOLOGY JUMP LOCI

Journal Article

10.
Full Text
The monodromy theorem for compact Kähler manifolds and smooth quasi-projective varieties

Mathematische Annalen, ISSN 0025-5831, 8/2018, Volume 371, Issue 3, pp. 1069 - 1086

Given any connected topological space X, assume that there exists an epimorphism $$\phi {:}\; \pi _1(X) \rightarrow {\mathbb {Z}}$$ ϕ:π1(X)→Z . The deck...

Mathematics, general | Mathematics | 32S40 | 14F45 | COMPLEMENTS | MATHEMATICS | COHOMOLOGY JUMP LOCI

Mathematics, general | Mathematics | 32S40 | 14F45 | COMPLEMENTS | MATHEMATICS | COHOMOLOGY JUMP LOCI

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2019, Volume 293, Issue 1, pp. 629 - 645

We revisit generic vanishing results for perverse sheaves with any field coefficients on a complex semi-abelian variety, and indicate several topological...

Semi-abelian variety | 14F17 | 14K12 | Character | 32S60 | Mathematics, general | Generic vanishing theorem | Integral Alexander module | Mathematics | Perverse sheaf | MATHEMATICS | PERVERSE SHEAVES | COHOMOLOGY JUMP LOCI

Semi-abelian variety | 14F17 | 14K12 | Character | 32S60 | Mathematics, general | Generic vanishing theorem | Integral Alexander module | Mathematics | Perverse sheaf | MATHEMATICS | PERVERSE SHEAVES | COHOMOLOGY JUMP LOCI

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2017, Volume 369, Issue 2, pp. 1309 - 1343

Given a finitely generated group \pi and a linear algebraic group G, the representation variety \mathrm {Hom}(\pi ,G) has a natural filtration by the...

Quasi-projective manifold | Differential graded algebra | Flat connection | Artin group | Characteristic variety | Lie algebra | Resonance variety | LOCAL SYSTEMS | INVARIANTS | quasi-projective manifold | JUMP LOCI | MATHEMATICS | COHOMOLOGY | characteristic variety | differential graded algebra | flat connection | GEOMETRY

Quasi-projective manifold | Differential graded algebra | Flat connection | Artin group | Characteristic variety | Lie algebra | Resonance variety | LOCAL SYSTEMS | INVARIANTS | quasi-projective manifold | JUMP LOCI | MATHEMATICS | COHOMOLOGY | characteristic variety | differential graded algebra | flat connection | GEOMETRY

Journal Article

Algebraic and Geometric Topology, ISSN 1472-2747, 03/2017, Volume 17, Issue 2, pp. 1163 - 1188

... groups, and for degree-1 topological Green-Lazarsfeld loci. As a corollary, we describe all regular surjections with connected generic fiber, defined on the above complements onto smooth complex curves of negative Euler characteristic...

Cohomology jump loci | Partial configuration space | Representation variety | Admissible maps onto curves | Gysin model | Malcev completion | Smooth projective curve | MATHEMATICS | LOCI | MODEL | RATIONAL HOMOTOPY-THEORY | ARRANGEMENTS

Cohomology jump loci | Partial configuration space | Representation variety | Admissible maps onto curves | Gysin model | Malcev completion | Smooth projective curve | MATHEMATICS | LOCI | MODEL | RATIONAL HOMOTOPY-THEORY | ARRANGEMENTS

Journal Article

Selecta Mathematica, ISSN 1022-1824, 10/2017, Volume 23, Issue 4, pp. 2331 - 2367

We explore the relationship between a certain “abelian duality” property of spaces and the propagation properties of their cohomology jump loci...

Propagation | 20J05 | Duality space | Mathematics | Hyperplane arrangement | Bestvina–Brady group | Resonance variety | Right-angled Artin group | Secondary 13C14 | 32S22 | Abelian duality space | Cohen–Macaulay property | Primary 55N25 | 55U30 | 57M07 | Mathematics, general | EPY property | Characteristic variety | 20F36 | Toric complex | ARTIN GROUPS | COMPLEMENTS | MATHEMATICS, APPLIED | RESOLUTIONS | VARIETIES | JUMP LOCI | MONOMIAL IDEALS | MATHEMATICS | Cohen-Macaulay property | COHOMOLOGY | Bestvina-Brady group | MILNOR FIBERS | HOMOLOGY | MORSE-THEORY | Algebra

Propagation | 20J05 | Duality space | Mathematics | Hyperplane arrangement | Bestvina–Brady group | Resonance variety | Right-angled Artin group | Secondary 13C14 | 32S22 | Abelian duality space | Cohen–Macaulay property | Primary 55N25 | 55U30 | 57M07 | Mathematics, general | EPY property | Characteristic variety | 20F36 | Toric complex | ARTIN GROUPS | COMPLEMENTS | MATHEMATICS, APPLIED | RESOLUTIONS | VARIETIES | JUMP LOCI | MONOMIAL IDEALS | MATHEMATICS | Cohen-Macaulay property | COHOMOLOGY | Bestvina-Brady group | MILNOR FIBERS | HOMOLOGY | MORSE-THEORY | Algebra

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2016, Volume 18, Issue 4, p. 1550065

.... The jump loci of rank one local systems on a normal variety are related to the jump loci of a resolution and of a smoothing of this variety.

Twisted cohomology | Local system | Normal variety | Characteristic variety | Fundamental group | TOPOLOGY | MATHEMATICS, APPLIED | fundamental group | INVARIANTS | PRESENTATIONS | COHOMOLOGY JUMP LOCI | MATHEMATICS | twisted cohomology | characteristic variety | local system | PROJECTIVE VARIETIES | SETS | SYSTEMS | GEOMETRY | Algebraic Geometry | Mathematics

Twisted cohomology | Local system | Normal variety | Characteristic variety | Fundamental group | TOPOLOGY | MATHEMATICS, APPLIED | fundamental group | INVARIANTS | PRESENTATIONS | COHOMOLOGY JUMP LOCI | MATHEMATICS | twisted cohomology | characteristic variety | local system | PROJECTIVE VARIETIES | SETS | SYSTEMS | GEOMETRY | Algebraic Geometry | Mathematics

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2015, Volume 65, Issue 2, pp. 549 - 603

The topology of smooth quasi-projective complex varieties is very restrictive. One aspect of this statement is the fact that natural strata of local systems, called cohomology support loci, have a rigid structure...

Monodromy Conjecture | Cohomology jump loci | Hyperplane arrangements | Alexander module | B-function | D-modules | Local systems | Bernstein-Sato ideal | Bernstein-Sato polynomial | Characteristic variety | Milnor fiber | Sabbah specialization | COMPLEMENTS | MONODROMY | ZETA-FUNCTIONS | INVARIANTS | B-FUNCTIONS | local systems | ALGORITHM | ANALYTIC-FUNCTIONS | POLYNOMIALS | MATHEMATICS | D-MODULE | characteristic variety | b-function | cohomology jump loci | hyperplane arrangements | HOMOLOGY

Monodromy Conjecture | Cohomology jump loci | Hyperplane arrangements | Alexander module | B-function | D-modules | Local systems | Bernstein-Sato ideal | Bernstein-Sato polynomial | Characteristic variety | Milnor fiber | Sabbah specialization | COMPLEMENTS | MONODROMY | ZETA-FUNCTIONS | INVARIANTS | B-FUNCTIONS | local systems | ALGORITHM | ANALYTIC-FUNCTIONS | POLYNOMIALS | MATHEMATICS | D-MODULE | characteristic variety | b-function | cohomology jump loci | hyperplane arrangements | HOMOLOGY

Journal Article

Geometry and Topology, ISSN 1465-3060, 03/2013, Volume 17, Issue 1, pp. 273 - 309

.... Such a space is stratified by the cohomology support loci of rank one local systems called characteristic varieties...

MATHEMATICS | CLASSIFICATION | LOCI | MODULI | LEFSCHETZ THEOREMS | GEOMETRY | Mathematics - Algebraic Geometry

MATHEMATICS | CLASSIFICATION | LOCI | MODULI | LEFSCHETZ THEOREMS | GEOMETRY | Mathematics - Algebraic Geometry

Journal Article

Advances in Mathematics, ISSN 0001-8708, 09/2018, Volume 335, pp. 231 - 260

...., the generic vanishing property and the signed Euler characteristic property hold, and the corresponding cohomology jump loci satisfy the propagation property and codimension lower bound...

Complex affine torus | Perverse sheaf | Cohomology jump loci | Abelian duality space | Generic vanishing | Mellin transformation | CONSTRUCTIBLE SHEAVES | ALGEBRAIC-GEOMETRY | DECOMPOSITION THEOREM | SEMIABELIAN VARIETIES | MATHEMATICS | PERVERSE SHEAVES | COMPACT KAHLER-MANIFOLDS | VANISHING THEOREMS

Complex affine torus | Perverse sheaf | Cohomology jump loci | Abelian duality space | Generic vanishing | Mellin transformation | CONSTRUCTIBLE SHEAVES | ALGEBRAIC-GEOMETRY | DECOMPOSITION THEOREM | SEMIABELIAN VARIETIES | MATHEMATICS | PERVERSE SHEAVES | COMPACT KAHLER-MANIFOLDS | VANISHING THEOREMS

Journal Article

19.
Full Text
Homological finiteness in the Johnson filtration of the automorphism group of a free group

Journal of Topology, ISSN 1753-8416, 12/2012, Volume 5, Issue 4, pp. 909 - 944

We examine the Johnson filtration of the (outer) automorphism group of a finitely generated group. In the case of a free group, we find a surprising result:...

MATHEMATICS | LOCI | COHOMOLOGY | COMPLETION

MATHEMATICS | LOCI | COHOMOLOGY | COMPLETION

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2009, Volume 220, Issue 2, pp. 441 - 477

... . We compute the cohomology jumping loci of the toric complex T L , as well as the homology groups of T L χ...

Cohomology ring | Holonomy Lie algebra | Malcev Lie algebra | Formality | Monodromy action | Artin kernel | Bestvina–Brady group | Stanley–Reisner ring | Toric complex | Right-angled Artin group | Cohomology jumping loci | Stanley-Reisner ring | Bestvina-Brady group | LOWER CENTRAL SERIES | MONOMIAL IDEALS | MATHEMATICS | ALGEBRAIC INVARIANTS | SIGMA-INVARIANTS | GRAPH GROUPS | HOMOLOGY

Cohomology ring | Holonomy Lie algebra | Malcev Lie algebra | Formality | Monodromy action | Artin kernel | Bestvina–Brady group | Stanley–Reisner ring | Toric complex | Right-angled Artin group | Cohomology jumping loci | Stanley-Reisner ring | Bestvina-Brady group | LOWER CENTRAL SERIES | MONOMIAL IDEALS | MATHEMATICS | ALGEBRAIC INVARIANTS | SIGMA-INVARIANTS | GRAPH GROUPS | HOMOLOGY

Journal Article

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