Cohopficity of seifert-bundle groups
A group G is cohopfian, if every monomorphism G → 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) ΠM is cohopfian; (b) M does not cover itself nontrivially; (c) M admits a geometric structure modeled on S3or on SL2R. If M is a compact Seifert bundle with nonempty boundary, then %iM is not cohopfian. © 1994 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
González-Acuñ, F., Litherland, R., & Whitten, W. (1994). Cohopficity of seifert-bundle groups. Transactions of the American Mathematical Society, 341 (1), 143-155. https://doi.org/10.1090/S0002-9947-1994-1123454-6