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In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant…

Algebraic Topology · Mathematics 2012-09-10 Jose Cantarero

We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps. We use this result to define an orbifold version of Bredon…

Algebraic Topology · Mathematics 2010-03-10 Dorette Pronk , Laura Scull

We describe a symmetry breaking construction in coarse geometry which allows to obtain information about equivariant coarse homology classes by restriction to smaller groups and spaces. In the case of equivariant coarse $K$-homology theory…

Algebraic Topology · Mathematics 2025-04-01 Ulrich Bunke , Matthias Ludewig

We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie…

dg-ga · Mathematics 2007-05-23 Michel Brion , Michèle Vergne

We introduce a bounded version of Bredon cohomology for groups relative to a family of subgroups. Our theory generalizes bounded cohomology and differs from Mineyev--Yaman's relative bounded cohomology for pairs. We obtain cohomological…

Group Theory · Mathematics 2023-05-17 Kevin Li

The main contribution of this paper is a generalization of several previous localization theories in equivariant symplectic geometry, including the classical Atiyah-Bott/Berline-Vergne localization theorem, as well as many cases of the…

Symplectic Geometry · Mathematics 2012-06-25 Megumi Harada , Yael Karshon

We obtain the equivariant K-homology of the classifying space \underline{E}SL(3,Z) from the computation of its Bredon homology with respect to finite subgroups and coefficients in the representation ring. We also obtain the corresponding…

K-Theory and Homology · Mathematics 2009-08-07 Ruben Sanchez-Garcia

Local cohomology techniques in equivariant homotopy theory, introduced by John Greenlees, may be applied to understand homology of classifying spaces through other equivariant data. In this paper we relate the local cohomology filtration to…

Algebraic Topology · Mathematics 2007-05-23 Dev Sinha

We develop a theory of equivariant factorization algebras on varieties with an action of a connected algebraic group $G$, extending the definitions of Francis-Gaitsgory [FG] and Beilinson-Drinfeld [BD1] to the equivariant setting. We define…

Representation Theory · Mathematics 2020-12-01 Dylan Butson

We prove simplicial version of a classical theorem of Eilenberg in the equivariant context and give an alternative description of the simplicial version of Bredon-Illman cohomology with local coefficients, as introduced in [15], to derive a…

Algebraic Topology · Mathematics 2015-03-17 Goutam Mukherjee , Debasis Sen

This thesis consists of two main parts. In the second part, we recall how a description of local coefficients that Eilenberg introduced in the 1940s leads to spectral sequences for the computation of homology and cohomology with local…

Algebraic Topology · Mathematics 2014-05-09 Megan Guichard Shulman

For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and…

Algebraic Topology · Mathematics 2009-03-10 Ioanid Rosu , Allen Knutson

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and…

K-Theory and Homology · Mathematics 2007-05-23 Christian Voigt

We prove equivariant versions of the Beilinson-Lichtenbaum conjecture for Bredon motivic cohomology of smooth complex and real varieties with an action of the group of order two. This identifies equivariant motivic and topological…

Algebraic Topology · Mathematics 2018-03-20 Jeremiah Heller , Mircea Voineagu , Paul Arne Ostvaer

We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like…

Algebraic Topology · Mathematics 2015-10-20 John Rognes , Steffen Sagave , Christian Schlichtkrull

The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially…

Commutative Algebra · Mathematics 2019-03-08 J. P. C. Greenlees

We introduce the notion of an E_k-ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories.…

Algebraic Topology · Mathematics 2025-06-11 John Rognes , Steffen Sagave , Christian Schlichtkrull

Using the description of the category of quasi-coherent sheaves on a root stack given in the paper of N. Borne and A. Vistoli, we study the G-theory of root stacks via localisation methods. We apply our results to the study of equivariant…

Algebraic Geometry · Mathematics 2019-08-14 A. Dhillon , I. Kobyzev

We use a spectral sequence developed by Graeme Segal in order to understand the twisted G-equivariant K-theory for proper and discrete actions. We show that the second page of this spectral sequence is isomorphic to a version of Bredon…

K-Theory and Homology · Mathematics 2021-03-08 Noe Barcenas , Jesus Espinoza , Bernardo Uribe , Mario Velasquez

We give two generalizations of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a…

Differential Geometry · Mathematics 2014-01-23 Andres Pedroza , Loring Tu