相关论文: Stringy K-theory and the Chern character

Given a henselian pair $(R, I)$ of commutative rings, we show that the relative $K$-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace $K \to \mathrm{TC}$. This yields a…

We extend the theorem of Hausel and the author from arXiv:2212.11836 that relates equivariant cohomology rings and algebras of functions on zero schemes. This paper combines three separate results. We prove that for a reductive group G…

We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

We study the operational bivariant theory associated to the covariant theory of Grothendieck groups of coherent sheaves, and prove that it has many geometric properties analogous to those of operational Chow theory. This operational…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type corresponding to the…

We construct the Schubert basis of the torus-equivariant K-homology of the affine Grassmannian of a simple algebraic group G, using the K-theoretic NilHecke ring of Kostant and Kumar. This is the K-theoretic analogue of a construction of…

The classical trace map is a highly non-trivial map from algebraic K-theory to topological Hochschild homology (or topological cyclic homology) introduced by B\"okstedt, Hsiang and Madsen. It led to many computations of algebraic K-theory…

It has been argued by Witten and others that in the presence of a nontrivial B-field, D-brane charges in type IIB string theories are measured by twisted K-theory. In joint work with Bouwknegt, Carey and Murray it was proved that twisted…

In this paper we construct a bivariant Chern character for the equivariant KK-theory of a totally disconnected group with values in bivariant equivariant cohomology in the sense of Baum and Schneider. We prove in particular that the…

Using symmetrized Grassmannians we give an algebraic geometric presentation, in the level of classifying spaces, of the Chern character and its relation to Chern classes. This allows one to define, for any projective variety $X$, a Chern…

We give a purely equivariant construction of orbifold products for quotient Deligne-Mumford stacks [X/G] where G is an arbitrary linear algebraic group (not necessarily finite). The key to our construction is the definition of the…

In this paper we construct a twisted version of quasi-elliptic cohomology. This theory can be constructed as a K-theory of a loop space. After establishing basic properties of the theory, including restriction, change-of-group and induction…

Given a compact Lie group $G$ acting on a space $X$, the classical Atiyah-Segal completion theorem identifies topological $K$-theory of the homotopy quotient $X/G$ with an explicit completion of $G$-equivariant topological $K$-theory of…

We give a construction for twisted equivariant K-theory in the case of a proper action of a discrete group using twisted bundles. Our construction uses results of Lueck and Oliver to extend a construction of Adem and Ruan. We also show the…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

We construct a relative version of the Crane-Yetter topological quantum field theory in four dimensions, from non-semisimple data. Our theory is defined relative to the classical $G$-gauge theory in five dimensions -- this latter theory…

In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted…

We demonstrate that twisted equivariant differential K-theory of transverse complex curves accommodates exotic charges of the form expected of codimension=2 defect branes, such as of D7-branes in IIB/F-theory on A-type orbifold…

We construct geometric models for classifying spaces of linear algebraic groups in G-equivariant motivic homotopy theory, where G is a tame group scheme. As a consequence, we show that the equivariant motivic spectrum representing the…