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CO-CONTRACTIONS OF GRAPHS AND RIGHT-ANGLED COXETER GROUPS

  • Kim, Jong-Tae ;
  • Moon, Myoung-Ho
  • Received : 2011.06.03
  • Published : 2012.09.30

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

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Cited by

  1. SURFACE SUBGROUPS OF GRAPH PRODUCTS OF GROUPS vol.22, pp.08, 2012, https://doi.org/10.1142/S0218196712400036

Acknowledgement

Supported by : Konkuk University