Related papers: Magnetic Equivariant K-theory

This paper examines and strengthens the Cuntz-Thomsen picture of equivariant Kasparov theory for arbitrary second-countable locally compact groups, in which elements are given by certain pairs of cocycle representations between C*-dynamical…

Let $\GR \to B$ be a bundle of compact Lie groups acting on a fiber bundle $Y \to B$. In this paper we introduce and study gauge-equivariant $K$-theory groups $K_\GR^i(Y)$. These groups satisfy the usual properties of the equivariant…

We review various aspects of the topological classification of D-brane charges in K-theory, focusing on techniques from geometric K-homology and Kasparov's KK-theory. The latter formulation enables an elaborate description of D-brane charge…

We introduce twisted permutation-equivariant GW-invariants, and compute them in terms of untwisted ones. The computation is based on Grothendieck-like RR formula corresponding to Adams' operations from K-theory to itself, and the result can…

"Quaternionic" vector bundles are the objects which describe the topological phases of quantum systems subjected to an odd time-reversal symmetry (class AII). In this work we prove that the FKMM invariant provides the correct fundamental…

We introduce two $K$-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these…

For an algebra B with an action of a Hopf algebra H we establish the pairing between even equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant…

We prove that "unitary deformation K-theory" takes products of finitely generated groups to coproducts of algebra spectra over ku, the connective K-theory spectrum. Additionally, we give spectral sequences for computing the homotopy groups…

The infinite matrix `Schwartz' group $G^{-\infty}$ is a classifying group for odd K-theory and carries Chern classes in each odd dimension, generating the cohomology. These classes are closely related to the Fredholm determinant on…

In the present paper we describe the action of (not necessarily line) bundles of finite order on the $K$-functor in terms of classifying spaces. This description might provide with an approach for more general twistings in $K$-theory than…

In this paper we study the "holomorphic K-theory" of a projective variety, which is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory was introduced by Lawson,…

This paper presents a comparison between two versions of Bott Periodicity Theorems: one in topological K-theory and the other in stable homotopy groups of classical groups. It begins with an introduction to K-theory, discussing vector…

We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…

Consider an action of a connected compact Lie group on a compact complex manifold $M$, and two equivariant vector bundles $L$ and $E$ on $M$, with $L$ of rank 1. The purpose of this paper is to establish holomorphic Morse inequalities \`{a}…

The point of this paper is to prove the conjecture that virtual 2-vector bundles are classified by K(ku), the algebraic K-theory of topological K-theory. Hence, by the work of Ausoni and the fourth author, virtual 2-vector bundles give us a…

We explore an approach to twisted generalized cohomology from the point of view of stable homotopy theory and quasicategory theory provided by arXiv:0810.4535. We explain the relationship to the twisted K-theory provided by Fredholm…

We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, matrix-stable, homotopy-invariant, excisive K-theory of algebras over a fixed unital ground ring H, kk_*(A,B),…

This work is devoted to the study of the foundations of quantum K-theory, a K-theoretic version of quantum cohomology theory. In particular, it gives a deformation of the ordinary K-ring K(X) of a smooth projective variety X, analogous to…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

Equivariant cohomology, a captivating fusion of symmetry and abstract mathematics, illuminates the profound role of group actions in shaping geometric structures. At its core lies the Atiyah-Bott Localization Theorem, a mathematical jewel…