NDLI: Self-coincidence numbers and the fundamental group

Content Provider	Springer Nature Link
Author	Gottlieb, Daniel Henry
Copyright Year	2007
Abstract	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 $$f : M \longrightarrow N$$ . We will 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, denoted $$\Lambda_{f,f}$$ , equals zero. Since $$\Lambda_{f,f}$$ is equal to the product of the degree of f and the Euler characteristic of N, we obtain results related to earlier results about the evaluation map and the Euler characteristic.
Starting Page	73
Ending Page	83
Page Count	11
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	2
Issue Number	1
e-ISSN	16617746
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2007-07-20
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Analysis Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

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Self-coincidence numbers and the fundamental group