Related papers: Twisted K-theory and loop groups
Equivariant $K$-theory is a generalized equivariant cohomology theory which is a hybrid of the $K$-theory of a topological space and the representation theory of the group acting on it. In this article, we review the basics of equivariant…
We compare different algebraic structures in twisted equivariant K-Theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-Theory, we prove a completion Theorem of Atiyah-Segal…
In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem…
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…
Let $G$ be a connected semisimple Lie group with its maximal compact subgroup $K$ being simply-connected. We show that the twisted equivariant $KK$-theory $KK^{\bullet}_{G}(G/K, \tau_G^G)$ of $G$ has a ring structure induced from the…
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…
We establish the twisted crystallographic T-duality, which is an isomorphism between Freed-Moore twisted equivariant K-groups of the position and momentum tori associated to an extension of a crystallographic group. The proof is given by…
We explore the relations of twisted K-theory to twisted and untwisted classical cohomology. We construct an Atiyah-Hirzebruch spectral sequence, and describe its differentials rationally as Massey products. We define the twisted Chern…
We present the fundamental properties of the K-theory groups of complex vector bundles endowed with actions of magnetic groups. In this work we show that the magnetic equivariant K-theory groups define an equivariant cohomology theory, we…
For $G$ a finite group, a normalized 2-cocycle $\alpha\in Z^{2}\big(G,{\mathbb S}^{1}\big)$ and $X$ a $G$-space on which a normal subgroup $A$ acts trivially, we show that the $\alpha$-twisted $G$-equivariant $K$-theory of $X$ decomposes as…
For G a finite group and X a G-space on which a normal subgroup A acts trivially, we show that the G-equivariant K-theory of X decomposes as a direct sum of twisted equivariant K-theories of X parametrized by the orbits of the conjugation…
We introduce twisted K-theoretic Gromov-Witten invariants - in the frameworks of both "ordinary" and permutation-equivariant K-theoretic GW theory defined recently by Givental. We focus on the case when the twisting is given by the Euler…
This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism…
Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also…
Twisted $K$-homology corresponds to $D$-branes in string theory. In this paper we compare two different models of geometric twisted $K$-homology and get their equivalence. Moreover, we give another description of geometric twisted…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Cohomologies of wrap groups…
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…
This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the…
The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to…