Co-contractions of graphs and right-angled Artin groups

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We define an operation on finite graphs, called co-contraction. Then we show that for any co-contraction (Gamma) over cap of a finite graph Gamma, the right-angled Artin group on Gamma contains a subgroup which is isomorphic to the right-angled Artin group on (Gamma) over cap. As a corollary, we exhibit a family of graphs, without any induced cycle of length at least 5, such that the right-angled Artin groups on those graphs contain hyperbolic surface groups. This gives the negative answer to a question raised by Gordon, Long and Reid.
Publisher
GEOMETRY TOPOLOGY PUBLICATIONS
Issue Date
2008
Language
English
Article Type
Article
Keywords

SURFACE SUBGROUPS; 3-MANIFOLDS; COHERENCE; COXETER

Citation

ALGEBRAIC AND GEOMETRIC TOPOLOGY, v.8, no.2, pp.849 - 868

ISSN
1472-2739
DOI
10.2140/agt.2008.8.849
URI
http://hdl.handle.net/10203/91135
Appears in Collection
MA-Journal Papers(저널논문)
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