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Volume 29, Issue 3


Tame combings and easy groups

Daniele Ettore Otera
  • Corresponding author
  • Mathematics and Informatics Institute of Vilnius University, Akademijos g. 4, LT-08663, Vilnius, Lithuania
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/ Valentin Poénaru
Published Online: 2016-08-11 | DOI: https://doi.org/10.1515/forum-2015-0063


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 [8]). What we prove is that such groups are easy (and hence QSF by [11]), 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 [8]), 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).

Keywords: Combings; quasi-simple filtration (QSF); inverse representations; easy groups

MSC 2010: 57M05; 57M10; 57N35


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About the article

Received: 2015-04-04

Published Online: 2016-08-11

Published in Print: 2017-05-01

Funding Source: European Science Foundation

Award identifier / Grant number: 6028

Funding Source: Lietuvos Mokslo Taryba

Award identifier / Grant number: MIP-046/2014/LSS-580000-446

The first author was partially supported by the ESF short-visit grant 6028 (within the Project ‘Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics – ITGP’), by INDAM of Italy, and by the Research Council of Lithuania Grant No. MIP-046/2014/LSS-580000-446 (Researcher teams’ projects).

Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 665–680, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0063.

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