Tame combings and easy groups
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Daniele Ettore Otera
und
Valentin Poénaru
Abstract
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).
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
Funding statement: 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).
Acknowledgements
The authors are thankful to Gérard Besson, Louis Funar, David Gabai, Frédéric Haglund and Corrado Tanasi for helpful conversations and comments on the subject. The first author wishes to thank the Laboratoire de Mathématiques d’Orsay (Université Paris-Sud 11) for the warm hospitality.
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© 2017 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Probabilistic trace and Poisson summation formulae on locally compact abelian groups
- The Selberg trace formula as a Dirichlet series
- On the cohomology and their torsion of real toric objects
- Outer automorphism groups of simple Lie algebras and symmetries of painted diagrams
- Non-abelian tensor and exterior products of multiplicative Lie rings
- On the infimum of the spectrum of a relativistic Schrödinger operator
- Character correspondences for symmetric groups and wreath products
- Univalence in locally cartesian closed ∞-categories
- On subordinate random walks
- Tame combings and easy groups
- On Belk’s classifying space for Thompson’s group F
- Subspace confinement for switched linear systems
- Exceptional bundles of homological dimension ${k}$
- Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces
- Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups
Artikel in diesem Heft
- Frontmatter
- Probabilistic trace and Poisson summation formulae on locally compact abelian groups
- The Selberg trace formula as a Dirichlet series
- On the cohomology and their torsion of real toric objects
- Outer automorphism groups of simple Lie algebras and symmetries of painted diagrams
- Non-abelian tensor and exterior products of multiplicative Lie rings
- On the infimum of the spectrum of a relativistic Schrödinger operator
- Character correspondences for symmetric groups and wreath products
- Univalence in locally cartesian closed ∞-categories
- On subordinate random walks
- Tame combings and easy groups
- On Belk’s classifying space for Thompson’s group F
- Subspace confinement for switched linear systems
- Exceptional bundles of homological dimension ${k}$
- Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces
- Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups
