Related papers: Mackey functors and classical equivariant $K$-theo…

Let $Q$ denote the cyclic group of order two. Using the Tate diagram we compute the $RO(Q)$-graded coefficients of Eilenberg-MacLane $Q$-spectra and describe their structure as a module over the coefficients of the Eilenberg-MacLane…

This paper studies the foundations of the geometric fixed point functor in multiplicative equivariant stable homotopy theory. We introduce a new class of equivariant orthogonal spectra called generalized orbit desuspension spectra and…

Thomason showed that the K-theory of symmetric monoidal categories models all connective spectra. This paper describes a new construction of a permutative category from a Gamma-space, which is then used to re-prove Thomason's theorem and a…

In a recent work Malkiewich and Merling proposed a definition of the equivariant $K$-theory of spaces for spaces equipped with an action of a finite group. We show that the fixed points of this spectrum admit a tom Dieck-type splitting. We…

In this paper we develop the basic homotopy theory of G-symmetric spectra (that is, symmetric spectra with a G-action) for a finite group G, as a model for equivariant stable homotopy with respect to a G-set universe. This model lies in…

Free and cofree equivariant spectra are important classes of equivariant spectra which represent equivariant cohomology theories on free equivariant spaces. Greenlees-Shipley and Pol and the author have given an algebraic model for rational…

We interpret certain equivariant Kasparov groups as equivariant representable K-theory groups. We compute these groups via a classifying space and as K-theory groups of suitable sigma-C*-algebras. We also relate equivariant vector bundles…

Equivariant homotopy methods developed over the last 20 years lead to recent breakthroughs in the Borel isomorphism conjectures for Loday assembly maps in K- and L-theories. An important consequence of these algebraic conjectures is the…

We prove the conjectures of Graham-Kumar and Griffeth-Ram concerning the alternation of signs in the structure constants for torus-equivariant K-theory of generalized flag varieties G/P. These results are immediate consequences of an…

Using the formalism of Grothendieck's derivators, we construct `the universal localizing invariant of dg categories'. By this, we mean a morphism U_l from the pointed derivator associated with the Morita homotopy theory of dg categories to…

Given a finite abelian group $G$ and a Sylow $p$-subgroup $N_p$, we prove that the $KU_G/p$-local sphere spectrum is equivalent to the homotopy fixed points of a $p$-complete $KO_{N_p}$-module spectrum. Then we compute the…

We consider analogs of Jacobson's $F$-Burnside construction and Boltje's $(-)_+$-construction for biset functors, using Mackey-functor theoretic interpretation of biset functors.

The twisted equivariant K-theory given by Freed and Moore is a K-theory which unifies twisted equivariant complex K-theory, Atiyah's `Real' K-theory, and their variants. In a general setting, we formulate this K-theory by using Fredholm…

We compute the homotopy Mackey functors of the $KU_G$-local equivariant sphere spectrum when $G$ is a finite $q$-group for an odd prime $q$, building on the degree zero case from arXiv:2204.03797.

We associate an invariant called the completed Tate cohomology to a filtered circle-equivariant spectrum and a complex oriented cohomology theory. We show that when the filtered spectrum is the spectral symplectic cohomology of a Liouville…

We compute the Borel equivariant cohomology ring of the left $K$-action on a homogeneous space $G/H$, where $G$ is a connected Lie group, $H$ and $K$ are closed, connected subgroups and $2$ and the torsion primes of the Lie groups are units…

We present an elementary construction of the non-connective algebraic K-theory spectrum associated to an additive category following the contracted functor approach due to Bass. It comes with a universal property that easily allows us to…

Using a combinatorial approach which avoids geometry, this paper studies the ring structure of K_T(G/B), the T-equivariant K-theory of the (generalized) flag variety G/B. Here the data is a complex reductive algebraic group (or…

We give a $K$-theoretic and geometric interpretation for a generalized weighted Ehrhart theory of a full-dimensional lattice polytope $P$, depending on a given homogeneous polynomial function $\varphi$ on $P$, and with Laurent polynomial…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…