Geometry & topology, ISSN 1465-3060, 2019, Volume 23, Issue 2, pp. 541 - 636

.... A similar result holds for calculating G-equivariant homotopy classes of maps into such spectra via an appropriate homotopy limit spectral sequence...

MATHEMATICS | LOCALIZATION | TATE COHOMOLOGY | EXTENSIONS | MACKEY FUNCTORS | EQUIVARIANT STABLE-HOMOTOPY | RING | K-THEORY | NILPOTENCY | HOMOLOGY | CLASSIFYING-SPACES

MATHEMATICS | LOCALIZATION | TATE COHOMOLOGY | EXTENSIONS | MACKEY FUNCTORS | EQUIVARIANT STABLE-HOMOTOPY | RING | K-THEORY | NILPOTENCY | HOMOLOGY | CLASSIFYING-SPACES

Journal Article

Journal of K-Theory, ISSN 1865-2433, 06/2014, Volume 13, Issue 3, pp. 563 - 599

.... The aim of this paper is to construct two spectral sequences for calculating these homology groups and to treat some concrete classes of examples such as Hochschild cochains, graded polynomial...

Hodge decomposition | Hochschild cohomology | Grothendieck spectral sequence | André-Quillen homology | En-homology | II-Algebras | E n -homology | Algebras | MATHEMATICS | Andre-Quillen homology | Pi-Algebras | COHOMOLOGY | LIE ALGEBRAS | SPACES | E-n-homology | HOPF ALGEBRAS

Hodge decomposition | Hochschild cohomology | Grothendieck spectral sequence | André-Quillen homology | En-homology | II-Algebras | E n -homology | Algebras | MATHEMATICS | Andre-Quillen homology | Pi-Algebras | COHOMOLOGY | LIE ALGEBRAS | SPACES | E-n-homology | HOPF ALGEBRAS

Journal Article

Topology and its applications, ISSN 0166-8641, 2019, Volume 267, p. 106901

... of a differential graded associative algebra. We also show that formality of a differential graded Lie algebra is not equivalent to the collapse of its associated Quillen spectral sequence. Finally, we use L...

Rational homotopy theory | [formula omitted]-algebra | Higher order Whitehead products | Coformality | Quillen spectral sequence | MATHEMATICS | MATHEMATICS, APPLIED | MODELS | PRODUCTS | SPACES | L-infinity-algebra | HOMOTOPY-THEORY

Rational homotopy theory | [formula omitted]-algebra | Higher order Whitehead products | Coformality | Quillen spectral sequence | MATHEMATICS | MATHEMATICS, APPLIED | MODELS | PRODUCTS | SPACES | L-infinity-algebra | HOMOTOPY-THEORY

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 1/2000, Volume 13, Issue 1, pp. 1 - 54

Integers | Universal coefficient theorem | Numbers | Algebra | Mathematical theorems | Maps | Real numbers | Mathematical rings | Mathematical duality | Motivic cohomology | Bloch-Lichtenbaum spectral sequence | Étale cohomology | Lichtenbaum-Quillen conjectures | Number fields | Two-primary algebraic K-theory | MATHEMATICS | MAIN CONJECTURE | COHOMOLOGY | TOTALLY-REAL FIELDS | EXTENSIONS | HOMOLOGY

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2007, Volume 215, Issue 1, pp. 250 - 262

Relying on the computation of the André–Quillen homology groups for unstable Hopf algebras, we prove that if the mod p cohomology of both the fiber and the...

H-space | Eilenberg–Moore spectral sequence | Steenrod algebra | Fibrations | André–Quillen homology | André-Quillen homology | Eilenberg-Moore spectral sequence | MATHEMATICS | Andre-Quillen homology | LOCALIZATION | ALGEBRAS | THEOREM | SULLIVAN | fibrations | HOMOLOGY | CLASSIFYING-SPACES

H-space | Eilenberg–Moore spectral sequence | Steenrod algebra | Fibrations | André–Quillen homology | André-Quillen homology | Eilenberg-Moore spectral sequence | MATHEMATICS | Andre-Quillen homology | LOCALIZATION | ALGEBRAS | THEOREM | SULLIVAN | fibrations | HOMOLOGY | CLASSIFYING-SPACES

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2017, Volume 11, Issue 1, pp. 225 - 307

In this paper, we define the equivariant eta form of Bismut-Cheeger for a compact Lie group and establish a formula about the functoriality of equivariant eta...

Equivariant eta form | Index theory and fixed point theory | Chern-Simons form | MATHEMATICS, APPLIED | index theory and fixed point theory | ELLIPTIC FAMILIES | ANALYTIC-TORSION FORMS | DIRAC OPERATORS | PHYSICS, MATHEMATICAL | QUILLEN METRICS | CHERN CHARACTER | SUPERCONNECTIONS | MATHEMATICS | SUBMERSIONS | IMMERSIONS | SPECTRAL ASYMMETRY | RIEMANNIAN GEOMETRY | Mathematics - Differential Geometry

Equivariant eta form | Index theory and fixed point theory | Chern-Simons form | MATHEMATICS, APPLIED | index theory and fixed point theory | ELLIPTIC FAMILIES | ANALYTIC-TORSION FORMS | DIRAC OPERATORS | PHYSICS, MATHEMATICAL | QUILLEN METRICS | CHERN CHARACTER | SUPERCONNECTIONS | MATHEMATICS | SUBMERSIONS | IMMERSIONS | SPECTRAL ASYMMETRY | RIEMANNIAN GEOMETRY | Mathematics - Differential Geometry

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2004, Volume 356, Issue 2, pp. 757 - 803

We construct a Taylor tower for functors from pointed categories to abelian categories via cotriples associated to cross effect functors. The tower was...

Towers | Algebra | Maps | Adjoints | Chain rule | Functors | Mathematics | Mathematical rings | Calculus | Algebraic topology | MATHEMATICS | FUNCTORS | SPECTRAL SEQUENCE | ANDRE-QUILLEN HOMOLOGY | STABILIZATION

Towers | Algebra | Maps | Adjoints | Chain rule | Functors | Mathematics | Mathematical rings | Calculus | Algebraic topology | MATHEMATICS | FUNCTORS | SPECTRAL SEQUENCE | ANDRE-QUILLEN HOMOLOGY | STABILIZATION

Journal Article

JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, ISSN 2193-8407, 2008, Volume 3, Issue 1, pp. 161 - 191

We explain how the approach of Andre and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories,...

MATHEMATICS | generalized (co)homology | homotopical algebra | Andre-Quillen cohomology | spectral sequences | ALGEBRA | algebras and theories | HOMOTOPY | BROWN REPRESENTABILITY | CATEGORIES

MATHEMATICS | generalized (co)homology | homotopical algebra | Andre-Quillen cohomology | spectral sequences | ALGEBRA | algebras and theories | HOMOTOPY | BROWN REPRESENTABILITY | CATEGORIES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2019, Volume 341, pp. 118 - 187

.... Topological Quillen homology, or TQ-homology, is the spectral algebra analog of Quillen homology and stabilization...

Homotopical descent | Symmetric spectra | Structured ring spectra | Operads | LOCALIZATION | ANDRE-QUILLEN COHOMOLOGY | SPACES | STABLE-HOMOTOPY | CALCULUS | MODEL CATEGORIES | PERIODIC HOMOLOGY | MATHEMATICS | MODULES | SEQUENCE | BAR CONSTRUCTIONS

Homotopical descent | Symmetric spectra | Structured ring spectra | Operads | LOCALIZATION | ANDRE-QUILLEN COHOMOLOGY | SPACES | STABLE-HOMOTOPY | CALCULUS | MODEL CATEGORIES | PERIODIC HOMOLOGY | MATHEMATICS | MODULES | SEQUENCE | BAR CONSTRUCTIONS

Journal Article

Topology, ISSN 0040-9383, 2005, Volume 44, Issue 6, pp. 1159 - 1179

We solve the homotopy limit problem for two-primary algebraic K-theory of fields, that is, the Quillen–Lichtenbaum conjecture at the prime 2.

Quillen–Lichtenbaum conjecture | Algebraic K-theory of fields | Étale and motivic cohomology | Spectral sequences | Homotopy fixed points | Quillen-Lichtenbaum conjecture | algebraic K-theory of fields | MATHEMATICS | homotopy fixed points | LOCALIZATION | spectral sequences | RINGS | BLOCH-KATO CONJECTURE | Etale and motivic cohomology

Quillen–Lichtenbaum conjecture | Algebraic K-theory of fields | Étale and motivic cohomology | Spectral sequences | Homotopy fixed points | Quillen-Lichtenbaum conjecture | algebraic K-theory of fields | MATHEMATICS | homotopy fixed points | LOCALIZATION | spectral sequences | RINGS | BLOCH-KATO CONJECTURE | Etale and motivic cohomology

Journal Article

Geometry and Topology, ISSN 1465-3060, 06/2013, Volume 17, Issue 3, pp. 1325 - 1416

Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of...

MATHEMATICS | SYMMETRIC SPECTRA | PLUS-CONSTRUCTION | LOCALIZATION | MODULES | COHOMOLOGY | STABLE-HOMOTOPY | CALCULUS | MODEL CATEGORIES | COMMUTATIVE S-ALGEBRAS | CONJECTURE | Mathematics - Algebraic Topology

MATHEMATICS | SYMMETRIC SPECTRA | PLUS-CONSTRUCTION | LOCALIZATION | MODULES | COHOMOLOGY | STABLE-HOMOTOPY | CALCULUS | MODEL CATEGORIES | COMMUTATIVE S-ALGEBRAS | CONJECTURE | Mathematics - Algebraic Topology

Journal Article

Topology, ISSN 0040-9383, 2003, Volume 42, Issue 1, pp. 197 - 225

In this paper we verify the strong Quillen–Lichtenbaum conjecture for integers in real number fields at the prime two. That is, we prove that the...

Galois module structure on units and Picard groups | Quillen–Lichtenbaum conjectures at the prime two (positive) étale cohomology | Homotopy fixed point spectral sequence | Quillen-Lichtenbaum conjectures at the prime two (positive) étale cohomology | LOCALIZATION | STABLE-HOMOTOPY | RINGS | CONJECTURES | ALGEBRAIC K-THEORY | Quillen-Lichtenbaum conjectures at the prime two (positive) etale cohomology | THEORY SPECTRUM | MATHEMATICS | COHOMOLOGY | INTEGERS | homotopy fixed point spectral sequence | COEFFICIENTS | HOMOLOGY

Galois module structure on units and Picard groups | Quillen–Lichtenbaum conjectures at the prime two (positive) étale cohomology | Homotopy fixed point spectral sequence | Quillen-Lichtenbaum conjectures at the prime two (positive) étale cohomology | LOCALIZATION | STABLE-HOMOTOPY | RINGS | CONJECTURES | ALGEBRAIC K-THEORY | Quillen-Lichtenbaum conjectures at the prime two (positive) etale cohomology | THEORY SPECTRUM | MATHEMATICS | COHOMOLOGY | INTEGERS | homotopy fixed point spectral sequence | COEFFICIENTS | HOMOLOGY

Journal Article

Mathematical Physics, Analysis and Geometry, ISSN 1385-0172, 6/2017, Volume 20, Issue 2, pp. 1 - 20

We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen’s original...

Geometry | Determinant line bundle | Quillen’s metric | Canonical trace | 58B34 | Theoretical, Mathematical and Computational Physics | Analysis | Noncommutative two torus | Group Theory and Generalizations | Applications of Mathematics | Physics | 46L87 | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | OPERATORS | 2-TORI | Quillen's metric | GEOMETRY | Algebra

Geometry | Determinant line bundle | Quillen’s metric | Canonical trace | 58B34 | Theoretical, Mathematical and Computational Physics | Analysis | Noncommutative two torus | Group Theory and Generalizations | Applications of Mathematics | Physics | 46L87 | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | OPERATORS | 2-TORI | Quillen's metric | GEOMETRY | Algebra

Journal Article

Topology, ISSN 0040-9383, 2001, Volume 40, Issue 5, pp. 993 - 1016

We describe algebraic obstruction theories for realizing an abstract (co)algebra K ∗ over the mod p Steenrod algebra as the (co)homology of a topological...

Quillen cohomology | (Co)homology ring | Cosimplicial resolution | Steenrod algebra | Realization | Unstable coalgebra | Cohomology operations | Primary 55S10 | Secondary 18G55 | OBSTRUCTIONS | cosimplicial resolution | CLASSIFICATION | realization | (Co)homology operations | MATHEMATICS | MODULES | COHOMOLOGY | unstable coalgebra | HOMOLOGY SPECTRAL SEQUENCE | cohomology ring | REALIZABILITY | COSIMPLICIAL SPACE | POLYNOMIAL ALGEBRAS | HOMOTOPY-GROUPS

Quillen cohomology | (Co)homology ring | Cosimplicial resolution | Steenrod algebra | Realization | Unstable coalgebra | Cohomology operations | Primary 55S10 | Secondary 18G55 | OBSTRUCTIONS | cosimplicial resolution | CLASSIFICATION | realization | (Co)homology operations | MATHEMATICS | MODULES | COHOMOLOGY | unstable coalgebra | HOMOLOGY SPECTRAL SEQUENCE | cohomology ring | REALIZABILITY | COSIMPLICIAL SPACE | POLYNOMIAL ALGEBRAS | HOMOTOPY-GROUPS

Journal Article

A K-teoria algébrica é um ramo da álgebra que associa para cada anel com unidade R, uma sequência de grupos abelianos chamados os n-ésimos K-grupos de R. Em...

Spectral sequences | K-teoria algébrica | Sequências espectrais | Bloch-Wigner exact sequence | Quillen's K-groups | Algebraic K-theory | K-grupos de Quillen | Sequência exata de Bloch-Wigner

Spectral sequences | K-teoria algébrica | Sequências espectrais | Bloch-Wigner exact sequence | Quillen's K-groups | Algebraic K-theory | K-grupos de Quillen | Sequência exata de Bloch-Wigner

Dissertation

K-Theory, ISSN 0920-3036, 05/1993, Volume 7, Issue 3, pp. 269 - 284

Journal Article

17.
Cyclic homology

1998, 2nd ed., Grundlehren der mathematischen Wissenschaften, ISBN 3540630740, Volume 301., xviii, 513

Book

Algebraic and Geometric Topology, ISSN 1472-2747, 11/2014, Volume 14, Issue 5, pp. 3021 - 3048

.... We discuss applications of these resolutions to spectral sequences for derived completions and Goodwillie calculus in general model categories.

MATHEMATICS | RING SPECTRA | FUNCTORS | HOMOLOGY | MODEL CATEGORIES

MATHEMATICS | RING SPECTRA | FUNCTORS | HOMOLOGY | MODEL CATEGORIES

Journal Article

Homology, Homotopy and Applications, ISSN 1532-0073, 2015, Volume 17, Issue 1, pp. 67 - 109

This paper aims to answer the following question: Given an adjunction between two categories, how is Quillen (co)homology in one category related to that in...

Adjunction | Quillen | Comparison | Model structure | Homology | Cohomology | Simplicial | MATHEMATICS | MATHEMATICS, APPLIED | homology | comparison | adjunction | cohomology | SIMPLICIAL COMMUTATIVE ALGEBRAS | simplicial | model structure | HOMOTOPY OPERATIONS

Adjunction | Quillen | Comparison | Model structure | Homology | Cohomology | Simplicial | MATHEMATICS | MATHEMATICS, APPLIED | homology | comparison | adjunction | cohomology | SIMPLICIAL COMMUTATIVE ALGEBRAS | simplicial | model structure | HOMOTOPY OPERATIONS

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2006, Volume 201, Issue 2, pp. 318 - 378

Let K ( n ) be the n th Morava K -theory at a prime p, and let T ( n ) be the telescope of a v n -self map of a finite complex of type n. In this paper we...

Goodwillie tower | Morava k-theory | Periodic homotopy | Infinite loop space | Topological Andre Quillen Homology | STABLE-HOMOTOPY THEORY | COMPLEX | UNIQUENESS | Goodwillic tower | MATHEMATICS | periodic homotopy | COHOMOLOGY | RING | EQUIVALENCES | infinite loop spaced | SPECTRA | LOOP-SPACES | MORAVA K-THEORIES

Goodwillie tower | Morava k-theory | Periodic homotopy | Infinite loop space | Topological Andre Quillen Homology | STABLE-HOMOTOPY THEORY | COMPLEX | UNIQUENESS | Goodwillic tower | MATHEMATICS | periodic homotopy | COHOMOLOGY | RING | EQUIVALENCES | infinite loop spaced | SPECTRA | LOOP-SPACES | MORAVA K-THEORIES

Journal Article

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