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When are Immersions Diffeomorphisms?

Published online by Cambridge University Press:  20 November 2018

Chung-Wu Ho
Chung-Wu Ho*
Affiliation:
Department of Mathematics, Statistics and Computer Science, Southern Illinois University at Edwardsville, Edwardsville, Il 62026
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Abstract

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It is shown in this paper that an immersion of a connected, closed n-manifold into another connected n-manifold is a diffeomorphism if and only if the induced homomorphism between the fundamental groups is surjective at some point. This is proved as a consequence of a more general assertion about topological spaces.

Keywords

57R5054C2557R4257N35Proper maplocal homeomorphismcovering projectionhomotopy lifting propertyunique path lifting property
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 491 - 492
Copyright
Copyright © Canadian Mathematical Society 1981

References

1.Ho, C., A note on proper maps, Proc. Amer. Math. Soc. SI (1975), 237-241. MR 51, #6698.Google Scholar