Related papers: Equivariant Universal Coefficient and Kunneth Spec…

We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of…

We define the equivariant Cox ring of a normal variety with algebraic group action. We study algebraic and geometric aspects of this object and show how it is related to the ordinary Cox ring. Then, we specialize to the case of normal…

We establish natural splittings for the values of global Mackey functors at orthogonal, unitary and symplectic groups. In particular, the restriction homomorphisms between the orthogonal, unitary and symplectic groups of adjacent dimensions…

Let G be a profinite group, {X_alpha}_alpha a cofiltered diagram of discrete G-spectra, and Z a spectrum with trivial G-action. We show how to define the homotopy fixed point spectrum F(Z, holim_alpha X_alpha)^{hG} and that when G has…

Suppose $G$ is a finite group. In this paper, we construct an equivalence between the $\infty$-category of algebras over an $N_{\infty}$-operad $\mathcal{O}$ associated to a $G$-indexing system $\mathcal{I}$ and the corresponding…

We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant…

We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…

We study equivariant coarse homology theories through an axiomatic framework. To this end we introduce the category of equivariant bornological coarse spaces and construct the universal equivariant coarse homology theory with values in the…

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for…

Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S…

For any finite group G, we construct a spectral sequence for computing the Bredon cohomology of a G-CW complex X, starting with the cohomology of X^H/\cup_{K>H}X^K with suitable local coefficients, for various H \leq G.

Let $G$ be a finite group. For a based $G$-space $X$ and a Mackey functor $M$, a topological Mackey functor $X\widetilde\otimes M$ is constructed, which will be called the stable equivariant abelianization of $X$ with coefficients in $M$.…

The main objective of this paper is to compute $RO(G)$-graded cohomology of $G$-orbits for the group $G=C_n$, where $n$ is a product of distinct primes. We compute these groups for the constant Mackey functor $\underline{Z}$ and for the…

The note identifies which which couniversal spaces have suspension spectra equivalent to commutative orthogonal ring G-spectra for a compact Lie group G. These are precisely those whose cofamily is closed under passage to finite index…

Recent work has applied scissors congruence $K$-theory to study classical cut-and-paste ($SK$) invariants of manifolds. This paper proves the conjecture that the squares $K$-theory of equivariant $SK$-manifolds arises as the fixed points of…

In this paper we extend equivariant infinite loop space theory to take into account multiplicative norms: For every finite group $G$, we construct a multiplicative refinement of the comparison between the $\infty$-categories of connective…

We describe the cohomology of the quotient Z_K/H of a moment-angle complex Z_K by a freely acting subtorus H in T^m by establishing a ring isomorphism of H*(Z_K/H,R) with an appropriate Tor-algebra of the face ring R[K], with coefficients…

In this paper, we view the equivariant orientation theory of equivariant vector bundles from the lenses of equivariant Picard spectra. This viewpoint allows us to identify, for a finite group $\mathrm{G}$, a precise condition under which an…

We identify the group of homomorphisms $\operatorname{Hom}_{\mathcal{GF}}(F,\mathbf{RU}_{\mathbb Q})$ in the category of ($\operatorname{fin}$)-global functors to the rationalization of the unitary representation ring functor and deduce…

This paper establishes a connection between equivariant ring spectra and Witt vectors in the sense of Dress and Siebeneicher. Given a commutative ringspectrum T in the highly structured sense, that is, an E-infinity-ringspectrum, with…