Self coincidence numbers and the fundamental group
| dc.creator | Gottlieb, Daniel Henry | |
| dc.date | 2007-02-08 | |
| dc.date | 2007-02-21 | |
| dc.date.accessioned | 2026-07-07T07:47:48Z | |
| dc.date.available | 2026-07-07T07:47:48Z | |
| dc.description | For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M,N;f) of continuous maps homotopic to f:M--> N.We show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence number of f equals zero. Since the self intersection number is equal to the product of the degree of f and the Euler--Poincare number of N, we obtain results related to earlier results about the evaluation map and the Euler--Poincare number. | |
| dc.description | 10 pages. his paper adds a hypothesis to Proposition 4.2 which renders it true. Thomas Schick found that the conjectures in section 4 were false. I added a revised conjecture, which Thomas Schick and Andreas Thom seem to have shown is true | |
| dc.identifier | https://arxiv.org/abs/math/0702236 | |
| dc.identifier | http://arxiv.org/abs/math/0702236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124289 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 55M20; 57R19; 20J05 | |
| dc.title | Self coincidence numbers and the fundamental group | |
| dc.type | text |