• Corpus ID: 119630845

Twisted K-theory

@article{Atiyah2004TwistedK,
  title={Twisted K-theory},
  author={Michael Francis Atiyah and Graeme B. Segal},
  journal={arXiv: K-Theory and Homology},
  year={2004}
}
Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C ∗ -algebras. Up to equivalence, the twisting corresponds to an element of H 3 (X; Z). We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary K-theory. (We omit, however, its relations to classical coho- mology, which we shall treat in a sequel.) We… 
Models of twisted K -theory
This thesis concerns geometrical models in complete generality of twistings in complex K-theory, in particular of higher twistings. In the first three chapters we treat the non-equivariant situation.
Twisted K theory of differentiable stacks
Abstract In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S 1 -gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott
The ring structure for equivariant twisted K-theory
Abstract We prove, under some mild conditions, that the equivariant twisted K-theory group of a crossed module admits a ring structure if the twisting 2-cocycle is 2-multiplicative. We also give an
Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class
Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as
Equivariant twisted Real K-theory of compact Lie groups
Abstract Let G be a compact, connected, and simply-connected Lie group viewed as a G -space via the conjugation action. The Freed–Hopkins–Teleman Theorem (FHT) asserts a canonical link between the
Loop groups and twisted K-theory III
In this paper, we identify the Ad-equivariant twisted K-theory of a compact Lie group G with the “Verlinde group” of isomorphism classes of admissible representations of its loop groups. Our
Twisted K-theory with coefficients in C*-algebras
We introduce a twisted version of $K$-theory with coefficients in a $C^*$-algebra $A$, where the twist is given by a new kind of gerbe, which we call Morita bundle gerbe. We use the description of
Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy
We consider twisted equivariant K-theory for actions of a compact Lie group G on a space X where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational
General plan of the paper
The motivation for this definition is to give in K-theory a satisfactory Thom isomorphism and Poincaré duality pairing which are analogous to the usual ones in cohomology with local coefficients.
Twisted K-theory 3
(0.1) Notation: Fix a separable Hilbert space H and denote by PU the projective unitary group of H , by Fred the space of Fredholm endomorphisms of H (both in the norm topology, unless otherwise
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 42 REFERENCES
Twisted K theory of differentiable stacks
Abstract In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S 1 -gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott
Equivariant K-theory
The purpose of this thesis is to present a fairly complete account of equivariant K-theory on compact spaces. Equivariant K-theory is a generalisation of K-theory, a rather well-known cohomology
Twisted K Theory Invariants
An invariant for twisted K theory classes on a 3-manifold is introduced. The invariant is then applied to the twisted equivariant classes arising from the supersymmetric Wess–Zumino–Witten model
Semi-infinite cohomology and string theory.
TLDR
The profound relation of semi-infinite cohomology theory to the gauge-invariant free string theory constructed by Banks and Peskin is revealed and the connection between gauge- Invariant interacting string theories and the geometric realizations of the infinite-dimensional Lie algebras is indicated.
On equivariant homotopy type
LET G BE a topological group. By a G-ANR we mean a separable and metrizable G-space X with the following property: whenever B is a normal G-space and A is an invariant closed subspace of B. any G-map
Twisted K-theory and loop groups
  • D. Freed
  • Mathematics, Materials Science
  • 2002
Twisted /("-theory has received much attention recently in both math­ ematics and physics. We describe some models of twisted /("-theory, both topological and geometric. Then we state a theorem which
Twisted K-Theory and K-Theory of Bundle Gerbes
Abstract: In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to
Analytic K-Homology
Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used
Topological Vector Spaces
Preface In the notion of a topological vector space, there is a very nice interplay between the algebraic structure of a vector space and a topology on the space, basically so that the vector space
CONTINUOUS-TRACE ALGEBRAS FROM THE BUNDLE THEORETIC POINT OF VIEW
Using various facts about principal bundles over a space, we give a unified treatment of several theorems about the structure of stable separable continuous-trace algebras, their automorphisms, and
...
1
2
3
4
5
...