Equivariant twisted Real K-theory of compact Lie groups

JOURNAL OF GEOMETRY AND PHYSICS

卷:124

Article

Fok, Chi-Kwong^1,2,3 

[1] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

[2] Natl Taiwan Univ, Natl Ctr Theoret Sci, Math Div, Taipei 10617, Taiwan

[3] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

关键词: Compact Lie groups;    KR-theory;    Verlinde algebra;    Real Spin(c) structure;   

DOI  :  10.1016/j.geomphys.2017.11.013

来源: Elsevier

【 摘 要 】

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 equivariant twisted K-homology of G and its Verlinde algebra. In this paper, we give a generalization of FHT in the presence of a Real structure of G. Along the way we develop preliminary materials necessary for this generalization, which are of independent interest in their own right. These include the definitions of Real Dixmier-Douady bundles, the Real third cohomology group which is shown to classify the former, and Real Spirt structures. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free