Direct image for multiplicative and relative $K$-theories from transgression of the families index theorem, part 1
| dc.creator | Berthomieu, Alain | |
| dc.date | 2006-11-09 | |
| dc.date | 2007-01-16 | |
| dc.date.accessioned | 2026-07-07T07:40:58Z | |
| dc.date.available | 2026-07-07T07:40:58Z | |
| dc.description | This paper contains the constructions of a real manifold version of relative K-theory, and of an extension of Karoubi's multiplicative K-theory suggested by U. Bunke (which I call ``free multiplicative K-theory'' in the sequel). Chern-Simons-Nadel type classes on relative K-theory are constructed, while it is proved that on free multiplicative K-theory, there is a notion of Chern-Weil character form, and of a Borel-type characteristic class (which is a differential form modulo exact forms) which recovers the classes $c_k$ of flat vector bundles studied by Bismut and Lott. Finally, a direct image for relative K-theory under proper submersion of compact orientable real manifolds is constructed. | |
| dc.description | Construction of the topological K-theoretic direct image representatives shortened, considerations added about fibral Hodge symmetry and name of ``transgressive K-theory'' changed to ''free multiplicative K-theory'' | |
| dc.identifier | https://arxiv.org/abs/math/0611281 | |
| dc.identifier | http://arxiv.org/abs/math/0611281 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121941 | |
| dc.subject | Differential Geometry | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 14F05; 19E20; 57R20 | |
| dc.title | Direct image for multiplicative and relative $K$-theories from transgression of the families index theorem, part 1 | |
| dc.type | text |