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FIXED POINT CHARACTERISATION FOR EXACT AND AMENABLE ACTION

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  16 June 2015

Z. DONG  and
Y. Y. WANG
Z. DONG
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China email [email protected]
Y. Y. WANG*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China email [email protected]
*
✉[email protected]
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Abstract

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Let $G$ be a finitely generated group acting on a compact Hausdorff space ${\mathcal{X}}$. We give a fixed point characterisation for the action being amenable. As a corollary, we obtain a fixed point characterisation for the exactness of $G$.

Keywords

amenable actionfixed pointexactness

MSC classification

Primary: 20F65: Geometric group theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 228 - 232
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Adams, S., ‘Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups’, Topology 33 (1994), 765–783.CrossRefGoogle Scholar
Anantharaman-Delaroche, C. and Renault, J., Amenable Groupoids, Monographies de L’Enseignement Mathématique, 36 (L’Enseignement Mathématique, Geneva, 2000).Google Scholar
Brodzki, J., Niblo, G. A., Nowak, P. and Wright, N., ‘Amenable actions, invariant means and bounded cohomology’, J. Topol. Anal. 321 (2012), 321–334.CrossRefGoogle Scholar
Day, M. M., ‘Fixed point theorems for compact convex sets’, Illinois J. Math. 5 (1961), 585–590; Correction: Illinois J. Math. 8 (1964), 713.CrossRefGoogle Scholar
Higson, N. and Roe, J., ‘Amenable group actions and the Novikov conjecture’, J. reine angew. Math. 519 (2000), 143–153.Google Scholar
Kirchberg, E. and Wassermann, S., ‘Exact groups and continuous bundles of C*-algebras’, Math. Ann. 315 (1999), 169–203.Google Scholar
Megginson, R. E., An Introduction to Banach Space Theory, Graduate Texts in Mathematics, 183 (Springer, New York, 1998).CrossRefGoogle Scholar
Ozawa, N., ‘Amenable actions and exactness for discrete groups’, C. R. Acad. Sci. Paris 330 (2000), 691–695.CrossRefGoogle Scholar