# The ring structure for equivariant twisted K-theory

@inproceedings{Tu2006TheRS, title={The ring structure for equivariant twisted K-theory}, author={Jean-Louis Tu and Ping Xu}, year={2006} }

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 explicit construction of the transgression map for any crossed module N → Γ and prove that any element in the image is ∞-multiplicative. As a consequence, we prove, under some mild conditions, for a crossed module N → Γ and any , that the equivariant twisted K-theory group admits a ring structure. As…

## 19 Citations

### Modular Invariants and Twisted Equivariant K-theory II: Dynkin diagram symmetries

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The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFT's associated to loop groups, as twisted…

### ON THE QUANTIZATION OF CONJUGACY CLASSES

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Let G be a compact, simple, simply connected Lie group. A theorem of Freed- Hopkins-Teleman identifies the level k� 0 fusion ring Rk(G) of G with the twisted equivariant K-homology at level k + h ∨ ,…

### Arbeitsgemeinschaft mit aktuellem Thema : Twisted K-theory Mathematisches Forschungsinstitut Oberwolfach October 8-14 , 2006 Organizers :

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### Modular Invariants and Twisted Equivariant K-theory

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Freed-Hopkins-Teleman expressed the Verlinde algebra as twisted equivariant K-theory. We study how to recover the full system (fusion algebra of defect lines), nimrep (cylindrical partition…

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We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant $PU(H)-$principle bundle. The construction is…

### Differential K-Theory: A Survey

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