Hopf algebroids and secondary characteristic classes
| dc.creator | Kaminker, Jerome | |
| dc.creator | Tang, Xiang | |
| dc.date | 2007-11-20 | |
| dc.date | 2007-12-04 | |
| dc.date.accessioned | 2026-07-07T08:46:40Z | |
| dc.date.available | 2026-07-07T08:46:40Z | |
| dc.description | We study a Hopf algebroid, $\calh$, naturally associated to the groupoid $U_n^δ\ltimes U_n$. We show that classes in the Hopf cyclic cohomology of $\calh$ can be used to define secondary characteristic classes of trivialized flat $U_n$-bundles. For example, there is a cyclic class which corresponds to the universal transgressed Chern character and which gives rise to the continuous part of the $ρ$-invariant of Atiyah-Patodi-Singer. Moreover, these cyclic classes are shown to extend to the K-theory of the associated $C^{*}$-algebra. This point of view gives leads to homotopy invariance results for certain characteristic numbers. In particular, we define a subgroup of the cohomology of a group analogous to the Gelfand-Fuchs classes described by Connes, \cite{connes:transverse}, and show that the higher signatures associated to them are homotopy invariant. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0711.3177 | |
| dc.identifier | http://arxiv.org/abs/0711.3177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143327 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Operator Algebras | |
| dc.title | Hopf algebroids and secondary characteristic classes | |
| dc.type | text |