Related papers: Exact cohomology sequences with integral coefficie…

Let $S$ denote the graded polynomial ring $\C[x_1,...,x_m]$. We interpret a chain complex of free $S$-modules having finite length homology modules as an $S^1$-equivariant map $\C^m\sm\{0\} \to X$, where $X$ is a moduli space of exact…

In this paper we introduce a common framework for describing the topological part of the Baum-Connes conjecture for a wide class of groups. We compute the Bredon homology for groups with aspherical presentation, one-relator quotients of…

We prove several completion theorems for equivariant K-theory and cyclic homology of schemes with group action over a field. One of these shows that for an algebraic space over a field acted upon by a linear algebraic group, the derived…

In this note, (rational) Betti numbers of homotopy colimits for toric diagrams and their classifying spaces are described in terms of sheaf cohomology over CW posets. We prove for any $T$-diagram $D$ over any CW poset that…

Let T be a torus, X a smooth quasi-compact separated scheme equipped with a T-action, and [X/T] the associated quotient stack. Given any localizing A1-homotopy invariant of dg categories E, we prove that the derived completion of E([X/T])…

For finite dimensional free $C_p$-spaces, the calculation of the Bredon cohomology ring as an algebra over the cohomology of $S^0$ is used to prove the non-existence of certain $C_p$-maps. These are related to Borsuk-Ulam type theorems, and…

We define equivariant projective unitary stable bundles as the appropriate twists when defining K-theory as sections of bundles with fibers the space of Fredholm operators over a Hilbert space. We construct universal equivariant projective…

We provide an equivariant extension of Carlsson's BGG correspondence in characteristic two. As an application we classify perfect cochain complexes of $(\mathbb{Z}/2\times \mathbb{Z}/2)\rtimes Q$-representations with four-dimensional total…

A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…

We introduce a notion of freeness for $RO$-graded equivariant generalized homology theories, considering spaces or spectra $E$ such that the $R$-homology of $E$ splits as a wedge of the $R$-homology of induced virtual representation…

Given a torus action on a compact space X, a fundamental result of Borel and Atiyah-Segal asserts that the equivariant cohomology of X is concentrated in the fixed locus X^T, up to inverting enough Chern classes. We prove an analogue for…

We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this…

We compute the equivariant $KO$-homology of the classifying space for proper actions of $\textrm{SL}_3(\mathbb{Z})$ and $\textrm{GL}_3(\mathbb{Z})$. We also compute the Bredon homology and equivariant $K$-homology of the classifying spaces…

We present the fundamental properties of the K-theory groups of complex vector bundles endowed with actions of magnetic groups. In this work we show that the magnetic equivariant K-theory groups define an equivariant cohomology theory, we…

We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…

Let X be a manifold with an action of a torus T such that all isotropy groups are connected and satisfying some other mild hypotheses. We provide a necessary and sufficient criterion for the T-equivariant cohomology of X with real…

Consider the Hamiltonian action of a torus on a compact twisted generalized complex manifold $M$. We first observe that Kirwan injectivity and surjectivity hold for ordinary equivariant cohomology in this setting. Then we prove that these…

We construct groups G that are virtually torsion-free and have virtual cohomological dimension strictly less than the minimal dimension for any model for the classifying space for proper actions of G. They are the first examples that have…

An \emph{affine subtorus} of the compact torus $T=(S^1)^n$ is a translated copy of a Lie subgroup. Given a finite collection $T_1,\ldots, T_k$ of such subtori, and a prime $p$, we describe an explicit chain complex that calculates the group…

We investigate the equivariant cohomology of the natural torus action on a K-contact manifold and its relation to the topology of the Reeb flow. Using the contact moment map, we show that the equivariant cohomology of this action is…