Geodesic
When are Immersions Diffeomorphisms?
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 491-492

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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.
DOI : 10.4153/CMB-1981-074-5
Mots-clés : 57R50, 54C25, 57R42, 57N35, Proper map, local homeomorphism, covering projection, homotopy lifting property, unique path lifting property 
Ho, Chung-Wu. When are Immersions Diffeomorphisms?. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 491-492. doi: 10.4153/CMB-1981-074-5
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     title = {When are {Immersions} {Diffeomorphisms?}},
     journal = {Canadian mathematical bulletin},
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     year = {1981},
     volume = {24},
     number = {4},
     doi = {10.4153/CMB-1981-074-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-074-5/}
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