2008/01/30 by Jesús A. Álvarez López, López, Jesús A. Álvarez, Yuri A. Kordyukov +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.0801.4628
29 pages
arxiv created 2008/01/30 · arxiv updated 2009/12/01
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)→(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.