Geometric cycles, index theory and twisted K-homology
| dc.creator | Wang, Bai-Ling | |
| dc.date | 2007-10-09 | |
| dc.date | 2008-07-09 | |
| dc.date.accessioned | 2026-07-07T09:48:55Z | |
| dc.date.available | 2026-07-07T09:48:55Z | |
| dc.description | We study twisted $Spin^c$-manifolds over a paracompact Hausdorff space $X$ with a twisting $α: X \to K(\ZZ, 3)$. We introduce the topological index and the analytical index on the bordism group of $α$-twisted $Spin^c$-manifolds over $(X, α)$, taking values in topological twisted K-homology and analytical twisted K-homology respectively. The main result of this paper is to establish the equality between the topological index and the analytical index. We also define a notion of geometric twisted K-homology, whose cycles are geometric cycles of $(X, \a)$ analogous to Baum-Douglas's geometric cycles. As an application of our twisted index theorem, we discuss the twisted longitudinal index theorem for a foliated manifold $(X, F)$ with a twisting $α: X \to K(\ZZ, 3)$, which generalizes the Connes-Skandalis index theorem for foliations and the Atiyah-Singer families index theorem to twisted cases. | |
| dc.description | Final version, 51 pages. To appear in Journal of Noncommutative Geometry | |
| dc.identifier | https://arxiv.org/abs/0710.1625 | |
| dc.identifier | http://arxiv.org/abs/0710.1625 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164393 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 19K56, 55N22, 58J22 | |
| dc.title | Geometric cycles, index theory and twisted K-homology | |
| dc.type | text |