Geodesic
Thompson’s group F and uniformly finite homology
Staley, Daniel1
1Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway NJ 08854-8019, USA
Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 2349-2360
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We use the uniformly finite homology developed by Block and Weinberger to study the geometry of the Cayley graph of Thompson’s group F. In particular, a certain class of subgraph of F is shown to be nonamenable (in the Følner sense). This shows that if the Cayley graph of F is amenable, these subsets, which include every finitely generated submonoid of the positive monoid of F, must necessarily have measure zero.

DOI : 10.2140/agt.2009.9.2349
Classification : 20F65, 05C25, 43A07
Keywords: Thompson's group F, uniformly finite homology, amenability

Staley, Daniel  1

1 Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway NJ 08854-8019, USA 
@article{10_2140_agt_2009_9_2349,
     author = {Staley, Daniel},
     title = {Thompson{\textquoteright}s group {F} and uniformly finite homology},
     journal = {Algebraic and Geometric Topology},
     pages = {2349--2360},
     year = {2009},
     volume = {9},
     number = {4},
     doi = {10.2140/agt.2009.9.2349},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.2349/}
}
TY  - JOUR
AU  - Staley, Daniel
TI  - Thompson’s group F and uniformly finite homology
JO  - Algebraic and Geometric Topology
PY  - 2009
SP  - 2349
EP  - 2360
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.2349/
DO  - 10.2140/agt.2009.9.2349
ID  - 10_2140_agt_2009_9_2349
ER  - 
%0 Journal Article
%A Staley, Daniel
%T Thompson’s group F and uniformly finite homology
%J Algebraic and Geometric Topology
%D 2009
%P 2349-2360
%V 9
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.2349/
%R 10.2140/agt.2009.9.2349
%F 10_2140_agt_2009_9_2349
Staley, Daniel. Thompson’s group F and uniformly finite homology. Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 2349-2360. doi: 10.2140/agt.2009.9.2349

[1] J Belk, Thompson’s Group F, PhD thesis, Cornell University (2004)

[2] I Benjamini, R Lyons, Y Peres, O Schramm, Group-invariant percolation on graphs, Geom. Funct. Anal. 9 (1999) 29

[3] J Block, S Weinberger, Aperiodic tilings, positive scalar curvature and amenability of spaces, J. Amer. Math. Soc. 5 (1992) 907

[4] M G Brin, C C Squier, Groups of piecewise linear homeomorphisms of the real line, Invent. Math. 79 (1985) 485

[5] J W Cannon, W J Floyd, W R Parry, Introductory notes on Richard Thompson’s groups, Enseign. Math. (2) 42 (1996) 215

[6] E Følner, On groups with full Banach mean value, Math. Scand. 3 (1955) 243

[7] I Namioka, Følner’s conditions for amenable semi-groups, Math. Scand. 15 (1964) 18

[8] A Y Ol’Shanskii, M V Sapir, Non-amenable finitely presented torsion-by-cyclic groups, Publ. Math. Inst. Hautes Études Sci. (2002)

[9] D Savchuk, Some graphs related to Thompson’s group F

Cité par Sources :