Related papers: K-theory of $\lambda$-rings and tensorlike functor…

Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…

Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…

We generalize to higher algebraic $K$-theory an identity (originally due to Milnor) that relates the Reidemeister torsion of an infinite cyclic cover to its Lefschetz zeta function. Our identity involves a higher torsion invariant, the…

A cohomology theory for lambda-rings is developed. This is then applied to study deformations of lambda-rings.

Let $k$ be a commutative ring with identity. A {\it $k$-plethory} is a commutative $k$-algebra $P$ together with a comonad structure $W_P$, called the {\it $P$-Witt ring} functor, on the covariant functor that it represents. We say that a…

In this paper, we first establish a K-theory version of the equivariant family index theorem for a circle action, then use it to prove several rigidity and vanishing theorems on the equivariant K-theory level.

We define a genuine $\mathbb{Z}/2$-equivariant real algebraic $K$-theory spectrum $KR(A)$, for every genuine $\mathbb{Z}/2$-equivariant spectrum $A$ equipped with a compatible multiplicative structure. This construction extends the real…

Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory tells that the ring of invariants A^G=H^0(G,A) is…

We prove a combinatorial rule for a complete decomposition, in terms of Langlands parameters, for representations of p-adic $GL_n$ that appear as parabolic induction from a large family (ladder representations). Our rule obviates the need…

We show that Mandell's inverse $K$-theory functor from $\Gamma$-categories to permutative categories preserves multiplicative structure. This is a first step towards an equivariant generalization that would be inverse to the construction of…

In this article we describe the equivariant and ordinary topological $K$-ring of a toric bundle with fiber a $T$-{\it cellular} toric variety. This generalizes the results in \cite{su} on $K$-theory of smooth projective toric bundles. We…

Tambara functors arise in equivariant homotopy theory as the structure adherent to the homotopy groups of a coherently commutative equivariant ring spectrum. We show that if $k$ is a field-like $C_{p^n}$-Tambara functor, then $k$ is the…

We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result…

We develop further the consequences of the irreducible-Boolean classification established in Ref. [9]; which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the…

We classify all invariants of the functor $I^n$ (powers of the fundamental ideal of the Witt ring) with values in $A$, that it to say functions $I^n(K)\rightarrow A(K)$ compatible with field extensions, in the cases where $A(K)=W(K)$ is the…

Boardman, Johnson, and Wilson gave a precise formulation for an unstable algebra over a generalized cohomology theory. Modifying their definition slightly in the case of complex K-theory by taking into account its periodicity, we prove that…

We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology $THH_{C_n}(-)$, and it describes the $E_2$ term of the K\"unneth spectral sequence for…

We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel…

In a previous paper we have introduced the gauge-equivariant K-theory group of a bundle endowed with a continuous action of a bundle of compact Lie groups. These groups are the natural range for the analytic index of a family of…

We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an \'etale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X.…