Semistability at the end of a group extension

Author:
Michael L. Mihalik

Journal:
Trans. Amer. Math. Soc. **277** (1983), 307-321

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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DOI:
https://doi.org/10.1090/S0002-9947-1983-0690054-4

Article copyright:
© Copyright 1983
American Mathematical Society