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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Proper actions on cohomology manifolds


Author: Harald Biller
Journal: Trans. Amer. Math. Soc. 355 (2003), 407-432
MSC (2000): Primary 57S10, 57S20; Secondary 57P05
Published electronically: September 6, 2002
MathSciNet review: 1928093
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Abstract | References | Similar Articles | Additional Information

Abstract: Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most $2$, then the group is effectively a Lie group.


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Additional Information

Harald Biller
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgarten- straße 7, 64289 Darmstadt, Germany
Email: biller@mathematik.tu-darmstadt.de

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03123-9
PII: S 0002-9947(02)03123-9
Keywords: proper action; cohomology manifold; orbit structure; dimension estimate; slice; Hilbert-Smith conjecture
Received by editor(s): November 30, 2001
Received by editor(s) in revised form: April 6, 2002
Published electronically: September 6, 2002
Article copyright: © Copyright 2002 American Mathematical Society