Semistability at the end of a group extension
Author:
Michael L. Mihalik
Journal:
Trans. Amer. Math. Soc. 277 (1983), 307321
MSC:
Primary 57M05; Secondary 20F32, 57M10
MathSciNet review:
690054
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Abstract: A ended complex, , is semistable at if all proper maps are properly homotopic. If and are finite complexes with isomorphic fundamental groups, then the universal cover of is semistable at if and only if the universal cover of is semistable at . Hence, the notion of a finitely presented group being semistable at is well defined. We prove Main Theorem. Let be a short exact sequence of finitely generated infinite groups. If is finitely presented, then is semistable at . Theorem. If and are locally compact, connected noncompact complexes, then is semistable at . Theorem. is semistable at . The proofs are geometrical in nature and the main tool is covering space theory.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198306900544
PII:
S 00029947(1983)06900544
Article copyright:
© Copyright 1983
American Mathematical Society
