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http://dx.doi.org/10.4134/BKMS.2012.49.5.1057

CO-CONTRACTIONS OF GRAPHS AND RIGHT-ANGLED COXETER GROUPS

Kim, Jong-Tae (Department of Mathematics Konkuk University)
Moon, Myoung-Ho (Department of Mathematics Education Konkuk University)

Publication Information

Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 1057-1065 More about this Journal

Abstract

We prove that if $\widehat{\Gamma}$ is a co-contraction of ${\Gamma}$ , then the right-angled Coxeter group $C(\widehat{\Gamma})$ embeds into $C({\Gamma})$ . Further, we provide a graph ${\Gamma}$ without an induced long cycle while $C({\Gamma})$ does not contain a hyperbolic surface group.

Keywords

right-angled Artin group; right-angled Coxeter group; hyperbolic surface subgroup;

Citations & Related Records

Reference

1	H. Servatius, C. Droms, and B. Servatius, Surface subgroups of graph group, Proc. Amer. Math. Soc. 106 (1989), no. 3, 573-578. DOI ScienceOn
2	G. Baumslag, Topics in Combinatorial Group Theory, Lectures in Mathematics ETH Zurich, Birkhauser Verlag, Basel, 1993.
3	R. W. Bell. Combinatorial methods for detecting surface subgroups in right-angled Artin groups, arxiv.org/1012.4208.
4	R. Charney, An introduction to right-angled Artin groups, Geom. Dedicata 125 (2007), 141-158. DOI
5	M. W. Davis and T. Januszkiewicz, Right-angled Artin groups are commensurable with right-angled Coxeter groups, J. Pure Appl. Algebra 153 (2000), no. 3, 229-235. DOI ScienceOn
6	C. McA. Gordon, D.D. Long, and A. W. Reid, Surface subgroups of Coxeter and Artin groups, J. Pure Appl. Algebra 189 (2004), no. 1-3, 135-148. DOI ScienceOn
7	J. Gross and T. W. Tucker, Topological Graph Theory, A Wiley-Interscience Publication, John Wiley and Sons, 1987.
8	S. Kim, Hyperbolic Surface Subgroups of Right-Angled Artin Groups and Graph Products of Groups, PhD thesis, Yale University, 2007.
9	S. Kim, Co-contractions of graphs and right-angled Artin groups, Algebr. Geom. Topol. 8 (2008), no. 2, 849-868. DOI
10	R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin, Heidelberg, New York, 1977.
11	W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory, Dover Publications Inc., 1976.
12	W. Massey, Algebraic Topology: An Introduction, GTM 56, Springer, 1977.
13	P. Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. (2) 17 (1978), no. 3, 555-565. DOI