Semistability at , -ended groups and group cohomology

Author:
Michael L. Mihalik

Journal:
Trans. Amer. Math. Soc. **303** (1987), 479-485

MSC:
Primary 20E06; Secondary 20J05, 57M10

MathSciNet review:
902779

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Abstract | References | Similar Articles | Additional Information

Abstract: A finitely presented group , is *semistable at* if for some (equivalently any) finite complex , with , any two proper maps ( the universal cover of ) that determine the same end of are properly homotopic in .

If is semistable at , then is free abelian. 0- and -ended groups are all semistable at .

Theorem. *If* *where* *is finite and* *and* *are finitely presented, semistable at* *groups, then* *is semistable at* .

Theorem. *If* *is an isomorphism between finite subgroups of the finitely presented semistable at* *group* , *then the resulting* *extension is semistable at* .

Combining these results with the accessibility theorem of M. Dunwoody gives

Theorem. *If all finitely presented* -*ended groups are semistable at* , *then all finitely presented groups are semistable at* .

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0902779-7

Article copyright:
© Copyright 1987
American Mathematical Society