Self coincidence numbers and the fundamental group

dc.creatorGottlieb, Daniel Henry
dc.date2007-02-08
dc.date2007-02-21
dc.date.accessioned2026-07-07T07:47:48Z
dc.date.available2026-07-07T07:47:48Z
dc.descriptionFor 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.description10 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.identifierhttps://arxiv.org/abs/math/0702236
dc.identifierhttp://arxiv.org/abs/math/0702236
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124289
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject55M20; 57R19; 20J05
dc.titleSelf coincidence numbers and the fundamental group
dc.typetext

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