On the vanishing of the Rokhlin invariant
| dc.creator | Moriyama, Tetsuhiro | |
| dc.date | 2008-07-14 | |
| dc.date.accessioned | 2026-07-07T09:50:12Z | |
| dc.date.available | 2026-07-07T09:50:12Z | |
| dc.description | It is a natural consequence of fundamental properties of the Casson invariant that the Rokhlin invariant of an amphichiral integral homology 3-sphere M vanishes. In this paper, we give a new direct proof of this vanishing property. For such an M, we construct a manifold pair (Y,Q) of dimensions 6 and 3 equipped with some additional structure (6-dimensional spin e-manifold), such that Q = M \cup M \cup (-M) and (Y,Q) \cong (-Y,-Q). We prove that (Y,Q) bounds a 7-dimensional spin e-manifold (Z,X) by studying the cobordism group of 6-dimensional spin e-manifolds and the Z/2-actions on the two--point configuration space of M minus one point. For any such (Z,X), the signature of X vanishes, and this implies the vanishing of the Rokhlin invariant. The idea of the construction of (Y,Q) comes from the definition of the Kontsevich-Kuperberg-Thurston invariant for rational homology 3-spheres. | |
| dc.description | 27 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0807.2195 | |
| dc.identifier | http://arxiv.org/abs/0807.2195 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164863 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27; 57N70, 57R20, 55R80 | |
| dc.title | On the vanishing of the Rokhlin invariant | |
| dc.type | text |