%0 Journal Article
%T Transversality and Lefschetz numbers for foliation maps
%A Jes¨˛s A. ¨˘lvarez L¨®pez
%A Yuri A. Kordyukov
%J Mathematics
%D 2008
%I arXiv
%X Let $F$ be a smooth foliation on a closed Riemannian manifold $M$, and let $\Lambda$ be a transverse invariant measure of $F$. Suppose that $\Lambda$ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then a topological definition of the $\Lambda$-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 $\Lambda$-Lefschetz number is equal to the analytic $\Lambda$-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 $F$.
%U http://arxiv.org/abs/0801.4628v1