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
DOI:
https://doi.org/10.1090/S0002-9947-1987-0902779-7
MathSciNet review:
902779
Full-text PDF Free Access
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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1987-0902779-7
Article copyright:
© Copyright 1987
American Mathematical Society