On Kontsevich's characteristic classes for smooth 5- and 7-dimensional homology sphere bundles
| dc.creator | Watanabe, Tadayuki | |
| dc.date | 2006-10-09 | |
| dc.date | 2007-04-23 | |
| dc.date.accessioned | 2026-07-07T07:57:42Z | |
| dc.date.available | 2026-07-07T07:57:42Z | |
| dc.description | M. Kontsevich constructed universal characteristic classes of smooth bundles with fiber a framed odd-dimensional integral homology sphere. In dimension 3, they are known to give a universal finite type invariants of homology 3-spheres. However, they have not been well understood for higher fiber dimensions. The purpose of the present paper is twofold. First, we obtain a bordism invariant of smooth unframed bundles with fiber a 5-dimensional homology sphere, which is defined as a sum of the simplest Kontsevich class and the second signature defect. It may be in some sense a higher dimensional analogue of the Casson invariant. Second, we construct a family of M-bundles. By evaluating on those M-bundles, we show that Kontsevich's universal characteristic classes are highly non-trivial in the case of fiber dimension 7. As a corollary, new estimates for unstable rational homotopy groups of Diff(D^7,\partial D^7) are obtained. | |
| dc.description | 31 pages, 9 figures, Corollary 4.4, 4.5 and detailed proof for Proposition 4.15 are added. Many typos are corrected. Proof of the IHX relation is removed because of an error | |
| dc.identifier | https://arxiv.org/abs/math/0610292 | |
| dc.identifier | http://arxiv.org/abs/math/0610292 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127739 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27, 55R35, 57R20 | |
| dc.title | On Kontsevich's characteristic classes for smooth 5- and 7-dimensional homology sphere bundles | |
| dc.type | text |