Transversality and Lefschetz numbers for foliation maps
| dc.creator | López, Jesús A. Álvarez | |
| dc.creator | Kordyukov, Yuri A. | |
| dc.date | 2008-01-30 | |
| dc.date.accessioned | 2026-07-07T08:57:16Z | |
| dc.date.available | 2026-07-07T08:57:16Z | |
| dc.description | Let $F$ be a smooth foliation on a closed Riemannian manifold $M$, and let $Λ$ be a transverse invariant measure of $F$. Suppose that $Λ$ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then a topological definition of the $Λ$-Lefschetz number of any leaf preserving diffeomorphism $(M,F)\to(M,F)$ is given. For this purpose, standard results about smooth approximation and transversality are extended to the case of foliation maps. It is asked whether this topological $Λ$-Lefschetz number is equal to the analytic $Λ$-Lefschetz number defined by Heitsch and Lazarov which would be a version of the Lefschetz trace formula. Heitsch and Lazarov have shown such a trace formula when the fixed point set is transverse to $F$. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/0801.4628 | |
| dc.identifier | http://arxiv.org/abs/0801.4628 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146902 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.title | Transversality and Lefschetz numbers for foliation maps | |
| dc.type | text |