Tame combings and easy groups

We consider finitely presented groups admitting 0-combings which are both Lipschitz (in the sense of Thurston) and tame (as defined by Mihalik and Tschantz in [ ]). What we prove is that such groups are easy (and hence QSF by [ ]), in the sense that they admit an easy representation (that is a map f...

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Bibliographic Details
Published inForum mathematicum Vol. 29; no. 3; pp. 665 - 680
Main Authors Otera, Daniele Ettore, Poénaru, Valentin
Format Journal Article
LanguageEnglish
Published De Gruyter 01.05.2017
Subjects
57M05
57M10
57N35
Combings
easy groups
inverse representations
quasi-simple filtration (QSF)
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Summary:We consider finitely presented groups admitting 0-combings which are both Lipschitz (in the sense of Thurston) and tame (as defined by Mihalik and Tschantz in [ ]). What we prove is that such groups are easy (and hence QSF by [ ]), in the sense that they admit an easy representation (that is a map from a 2-complex to a singular 3-manifold associated to the group, satisfying several topological conditions with a strong control over singularities). Besides its own interest, one may also try to adapt the proof in a wider context, namely for groups admitting tame 1-combings (as in [ ]), in order to prove the easy-representability for a larger class of finitely presented groups (note that there are still no examples of finitely presented groups which are not tame 1-combable).
ISSN:0933-7741
1435-5337
DOI:10.1515/forum-2015-0063