논문KCI 등재
CO-CONTRACTIONS OF GRAPHS AND RIGHT-ANGLED COXETER GROUPS
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초록
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.
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.
참고문헌 (13)
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- J. Gross, "Topological Graph Theory" (1987), A Wiley-Interscience Publication, John Wiley and Sons
- S. Kim, "Hyperbolic Surface Subgroups of Right-Angled Artin Groups and Graph Products of Groups", 박사, pp.2007
- 김상현, "Co-contractions of graphs and right-angled Artin groups", ALGEBRAIC AND GEOMETRIC TOPOLOGY, 8(2), pp.849~868 (2008), GEOMETRY TOPOLOGY PUBLICATIONS
- R. C. Lyndon, "Combinatorial Group Theory" (1977), Springer
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- P. Scott, "Subgroups of surface groups are almost geometric", J. London Math. Soc. (2), 17(3), pp.555~565 (1978)
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