Physics Letters B, ISSN 0370-2693, 07/2018, Volume 782, pp. 94 - 98

In the Standard Model, the electroweak symmetry is broken by a complex, SU(2)-doublet Higgs field and the vacuum manifold SU(2)×U(1)/U(1) has the topology of a...

STRINGS | PHYSICS, NUCLEAR | PHENOMENOLOGICAL LAGRANGIANS | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Phenomenology | High Energy Physics | Physics

STRINGS | PHYSICS, NUCLEAR | PHENOMENOLOGICAL LAGRANGIANS | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Phenomenology | High Energy Physics | Physics

Journal Article

Selecta Mathematica, ISSN 1022-1824, 4/2018, Volume 24, Issue 2, pp. 1453 - 1478

We compute the groups $$H^*(\mathrm {Aut}(F_n); M)$$ H∗(Aut(Fn);M) and $$H^*(\mathrm {Out}(F_n); M)$$ H∗(Out(Fn);M) in a stable range, where M is obtained by...

Homology stability | Automorphisms of free groups | 20J06 | Mathematics, general | 20F28 | Mathematics | 57R20 | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | HOMOLOGY | SURFACES | GRAPHS

Homology stability | Automorphisms of free groups | 20J06 | Mathematics, general | 20F28 | Mathematics | 57R20 | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | HOMOLOGY | SURFACES | GRAPHS

Journal Article

Mathematische Annalen, ISSN 0025-5831, 8/2017, Volume 368, Issue 3, pp. 1081 - 1094

We prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than $$(2n-2)$$ ( 2 n - 2 ) . In order to do so, we define new...

Mathematics, general | Mathematics | MATHEMATICS | HIGH-DIMENSIONAL MANIFOLDS | FIBRATIONS | SPACES | HOMOTOPY-THEORY | POINCARE-DUALITY

Mathematics, general | Mathematics | MATHEMATICS | HIGH-DIMENSIONAL MANIFOLDS | FIBRATIONS | SPACES | HOMOTOPY-THEORY | POINCARE-DUALITY

Journal Article

Selecta Mathematica, ISSN 1022-1824, 9/2018, Volume 24, Issue 4, pp. 3835 - 3873

We prove several basic ring-theoretic results about tautological rings of manifolds W, that is, the rings of generalised Miller–Morita–Mumford classes for...

57S25 | 57R22 | 55R10 | Mathematics, general | Mathematics | 55R40 | 57R20 | MATHEMATICS | JACOBIAN MANIFOLDS | MATHEMATICS, APPLIED | CIRCLE ACTIONS | FAMILIES | SURFACE BUNDLES | 4-MANIFOLDS | HOMOLOGY | MAP

57S25 | 57R22 | 55R10 | Mathematics, general | Mathematics | 55R40 | 57R20 | MATHEMATICS | JACOBIAN MANIFOLDS | MATHEMATICS, APPLIED | CIRCLE ACTIONS | FAMILIES | SURFACE BUNDLES | 4-MANIFOLDS | HOMOLOGY | MAP

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 01/2018, Volume 31, Issue 1, pp. 215 - 264

We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension 2n > 4, with respect to forming connected sum with S^n...

MATHEMATICS | MAPPING CLASS-GROUPS | SURFACES

MATHEMATICS | MAPPING CLASS-GROUPS | SURFACES

Journal Article

Annals of Mathematics, ISSN 0003-486X, 7/2017, Volume 186, Issue 1, pp. 127 - 204

We prove a homological stability theorem for moduli spaces of manifolds of dimension 2n, for attaching handles of index at least n, after these manifolds have...

Morphisms | Mathematical manifolds | Maps | Mathematical theorems | Functors | Mathematics | Topology | Coefficients | Vertices | Topological spaces | Moduli spaces | Characteristic classes | Homological stability | Diffeomorphism groups | moduli spaces | diffeomorphism groups | MATHEMATICS | homological stability | characteristic classes | HOMOTOPY | SURFACES

Morphisms | Mathematical manifolds | Maps | Mathematical theorems | Functors | Mathematics | Topology | Coefficients | Vertices | Topological spaces | Moduli spaces | Characteristic classes | Homological stability | Diffeomorphism groups | moduli spaces | diffeomorphism groups | MATHEMATICS | homological stability | characteristic classes | HOMOTOPY | SURFACES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2017, Volume 318, pp. 534 - 626

Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose...

Automorphism groups | Homological stability | Mapping class groups | Braid groups | General linear groups | Unitary groups | NONORIENTABLE SURFACE | BRAID-GROUPS | RINGS | TWISTED COEFFICIENTS | GROUP-COMPLETION | MAPPING CLASS-GROUPS | LINEAR-GROUPS | MATHEMATICS | CONFIGURATION-SPACES | SYMMETRIC-GROUPS | FI-MODULES

Automorphism groups | Homological stability | Mapping class groups | Braid groups | General linear groups | Unitary groups | NONORIENTABLE SURFACE | BRAID-GROUPS | RINGS | TWISTED COEFFICIENTS | GROUP-COMPLETION | MAPPING CLASS-GROUPS | LINEAR-GROUPS | MATHEMATICS | CONFIGURATION-SPACES | SYMMETRIC-GROUPS | FI-MODULES

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 9/2017, Volume 209, Issue 3, pp. 749 - 835

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there...

58J20 | 57R90 | 58D17 | 58D05 | 19K56 | 53C27 | Mathematics | 57R65 | 19D06 | 55R35 | 55S35 | 57R22 | 55P47 | Mathematics, general | HOMOTOPY TYPE | MATHEMATICS | THEOREM | SIMPLY CONNECTED MANIFOLDS | METRICS | CLASSIFICATION | INDEX | Theorems | Homotopy theory | Manifolds (mathematics) | Curvature

58J20 | 57R90 | 58D17 | 58D05 | 19K56 | 53C27 | Mathematics | 57R65 | 19D06 | 55R35 | 55S35 | 57R22 | 55P47 | Mathematics, general | HOMOTOPY TYPE | MATHEMATICS | THEOREM | SIMPLY CONNECTED MANIFOLDS | METRICS | CLASSIFICATION | INDEX | Theorems | Homotopy theory | Manifolds (mathematics) | Curvature

Journal Article

Acta Mathematica, ISSN 0001-5962, 6/2014, Volume 212, Issue 2, pp. 257 - 377

We prove an analogue of the Madsen–Weiss theorem for high-dimensional manifolds. In particular, we explicitly describe the ring of characteristic classes of...

57R15 | 57R90 | 57S05 | 55P47 | Mathematics, general | Mathematics | 57R65 | 57R20 | 57R50 | MATHEMATICS | CATEGORY | Manifolds | Analogue | Fibres | Texts | Homology | Polynomials | Bundles | Rings (mathematics)

57R15 | 57R90 | 57S05 | 55P47 | Mathematics, general | Mathematics | 57R65 | 57R20 | 57R50 | MATHEMATICS | CATEGORY | Manifolds | Analogue | Fibres | Texts | Homology | Polynomials | Bundles | Rings (mathematics)

Journal Article

ISSN 1022-1824, 2018

We prove several basic ring-theoretic results about tautological rings of manifolds W, that is, the rings of generalised Miller–Morita–Mumford classes for...

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 1, pp. 1 - 81

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem...

Moduli spaces | Homological stability | Mapping class groups | moduli spaces | MATHEMATICS | MATHEMATICS, APPLIED | R-SPIN | RIEMANN SURFACES | MAPPING CLASS GROUP | mapping class groups

Moduli spaces | Homological stability | Mapping class groups | moduli spaces | MATHEMATICS | MATHEMATICS, APPLIED | R-SPIN | RIEMANN SURFACES | MAPPING CLASS GROUP | mapping class groups

Journal Article

ISSN 0020-9910, 2017

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there...

Journal Article

ISSN 0025-5831, 2017

We prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than (2n - 2). In order to do so, we define new characteristic...

Journal Article

14.
Full Text
Infinite loop spaces and positive scalar curvature in the presence of a fundamental group

Geometry & Topology, ISSN 1465-3060, 05/2019, Volume 23, Issue 3, pp. 1549 - 1610

Geom. Topol. 23 (2019) 1549-1610 This is a continuation of our previous work with Botvinnik on the nontriviality of the secondary index invariant on spaces of...

Journal Article

ISSN 1022-1824, 2017

We compute the groups H*(Aut(F$_{n}$);M) and H*(Out(F$_{n}$);M) in a stable range, where M is obtained by applying a Schur functor to H$_{Q}$ or H$_{Q}$,...

automorphisms of free groups | homology stability

automorphisms of free groups | homology stability

Journal Article

ISSN 0370-2693, 2018

In the Standard Model, the electroweak symmetry is broken by a complex, $SU(2)$-doublet Higgs field and the vacuum manifold $SU(2)\times U(1)/U(1)$ has the...

Journal Article

Quarterly Journal of Mathematics, ISSN 0033-5606, 03/2013, Volume 64, Issue 1, pp. 303 - 326

This paper consists of two related parts. In the first part we give a self-contained proof of homological stability for the spaces C-n(M; X) of configurations...

MATHEMATICS | Mathematics - Algebraic Topology

MATHEMATICS | Mathematics - Algebraic Topology

Journal Article

Mathematical Proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 05/2013, Volume 154, Issue 3, pp. 419 - 438

We study the cohomology of the space of immersed genus g surfaces in a simply-connected manifold. We compute the rational cohomology of this space in a stable...

MATHEMATICS | MAPPING CLASS GROUP | Topological manifolds | Theorems | Manifolds | Mathematical models | Infinity | Torsion | Mathematics - Algebraic Topology

MATHEMATICS | MAPPING CLASS GROUP | Topological manifolds | Theorems | Manifolds | Mathematical models | Infinity | Torsion | Mathematics - Algebraic Topology

Journal Article

ALGEBRAIC AND GEOMETRIC TOPOLOGY, ISSN 1472-2739, 2019, Volume 19, Issue 4, pp. 2099 - 2150

This is an exposition of homotopical results on the geometric realisation of semi-simplicial spaces. We then use these to derive basic foundational results...

MATHEMATICS | STABLE MODULI SPACES | GROUP-COMPLETION

MATHEMATICS | STABLE MODULI SPACES | GROUP-COMPLETION

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2012, Volume 231, Issue 3-4, pp. 1773 - 1785

We give a simple generalisation of a theorem of Morita (1989) [10,11], which leads to a great number of relations among tautological classes on moduli spaces...

Moduli spaces | Tautological algebra | MATHEMATICS | JACOBIAN MANIFOLDS | STABILITY | FAMILIES | ALGEBRA | RING | SURFACE BUNDLES | MAPPING CLASS-GROUPS | CURVES | MODULI

Moduli spaces | Tautological algebra | MATHEMATICS | JACOBIAN MANIFOLDS | STABILITY | FAMILIES | ALGEBRA | RING | SURFACE BUNDLES | MAPPING CLASS-GROUPS | CURVES | MODULI

Journal Article

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