On the actions of Higman-Thompson groups by homeomorphisms
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The aim of this short paper is to show some rigidity results for the actions of certain finitely presented groups by homeomorphisms. As an interesting and special case, we show that the actions of Higman-Thompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the well-known Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.
Abstract
The aim of this short paper is to show some rigidity results for the actions of certain finitely presented groups by homeomorphisms. As an interesting and special case, we show that the actions of Higman-Thompson groups by homeomorphisms on a cohomology manifold with a non-zero Euler characteristic should be trivial. This is related to the well-known Zimmer program and shows that the actions by homeomorphism could be very much different from those by diffeomorphisms.
참고문헌 (11)
- Goulnara Arzhantseva, "Infinite groups with fixed point properties", Geometry & Topology, 13(3), pp.1229~1263 (2009), Mathematical Sciences Publishers[DOI]
- A. Borel, "Seminar on Transformation Groups" (1960), Princeton University Press
- G. E. Bredon, "Sheaf Theory" (1997), Springer-Verlag
- M. R. Bridson, "Actions of automorphism groups of free groups on homology spheres and acyclic manifolds", Comment. Math. Helv, 86(1), pp.73~90 (2011)[DOI]
- D. Fisher, "Geometry, rigidity, and group actions", pp.72~157 (2011), Univ. Chicago Press
- G. Higman, "Finitely presented infinite simple groups", Department of Pure Mathematics, pp.1974
- K. Kawakubo, "The Theory of Transformation Groups" (1991), The Clarendon Press
- L. N. Mann, "Actions of Elementary P-Groups on Manifolds", Transactions of the American Mathematical Society, 106(1), pp.115~126 (1963), JSTOR[DOI]
- Claas E. Röver, "Constructing Finitely Presented Simple Groups That Contain Grigorchuk Groups", Journal of Algebra, 220(1), pp.284~313 (1999), Elsevier BV[DOI]
- Dave Witte, "Arithmetic Groups of Higher ℚ-Rank Cannot Act on 1-Manifolds", Proceedings of the American Mathematical Society, 122(2), pp.333~340 (1994), JSTOR[DOI]
- Shengkui Ye, "Euler characteristics and actions of automorphism groups of free groups", Algebraic & Geometric Topology, 18(2), pp.1195~1204 (2018), Mathematical Sciences Publishers[DOI]