2007/02/08 by Daniel Henry Gottlieb, Gottlieb, Daniel Henry
Mathematics · #20J05 #55M20 #57R19 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:20J05 #msc:55M20 #msc:57R19
paper · pdf · doi:10.48550/arxiv.math/0702236
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
openalex publication_date 2007/02/08 · arxiv created 2007/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.