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Orbifold index and equivariant K-homology
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bunke, Ulrich |
| Copyright Year | 2007 |
| Abstract | Let G be countable group and M be a proper cocompact even-dimensional Gmanifold with orbifold quotient M̄ . Let D be a G-invariant Dirac operator on M . It induces an equivariant K-homology class [D] ∈ KG 0 (M) and an orbifold Dirac operator D̄ on M̄ . Composing the assembly map KG 0 (M) → K0(C ∗(G)) with the homomorphism K0(C ∗(G)) → Z given by the representation C∗(G) → C of the maximal group C∗-algebra induced from the trivial representation of G we define index([D]) ∈ Z. In the second section of the paper we show that index(D̄) = index([D]) and obtain explicit formulas for this integer. In the third section we review the decomposition of KG 0 (M) in terms of the contributions of fixed point sets of finite cyclic subgroups of G obtained by W. Lück. In particular, the class [D] decomposes in this way. In the last section we derive an explicit formula for the contribution to [D] associated to a finite cyclic subgroup of G. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0701768v3.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0701768v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0701768v1.pdf |
| Alternate Webpage(s) | http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/Bunke/khom.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Dirac operator Fixed point (mathematics) Fixed-Point Number Homologous Gene Homology (biology) Integer (number) Kasparov's Gambit Maximal set Subgroup A Nepoviruses |
| Content Type | Text |
| Resource Type | Article |
