Co-Hopficity of Seifert-bundle groups
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- by F. González-Acuña, R. Litherland and W. Whitten
- Trans. Amer. Math. Soc. 341 (1994), 143-155
- DOI: https://doi.org/10.1090/S0002-9947-1994-1123454-6
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Abstract:
A group $G$ is cohopfian, if every monomorphism $G \to G$ is an automorphism. In this paper, we answer the cohopficity question for the fundamental groups of compact Seifert fiber spaces (or Seifert bundles, in the current vernacular). If $M$ is a closed Seifert bundle, then the following are equivalent: (a) ${\pi _1}M$ is cohopfian; (b) $M$ does not cover itself nontrivially; (c) $M$ admits a geometric structure modeled on ${S^3}$ or on ${\tilde {\text {SL}_2\mathbf {R}}}$. If $M$ is a compact Seifert bundle with nonempty boundary, then ${\pi _1}M$ is not cohopfian.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 341 (1994), 143-155
- MSC: Primary 57M05; Secondary 20C99, 55R05, 55R10, 57N10
- DOI: https://doi.org/10.1090/S0002-9947-1994-1123454-6
- MathSciNet review: 1123454