Description
The motivation for this talk is Gromov’s famous surface subgroup question: Does every one-ended hyperbolic group contain a subgroup which is isomorphic to the fundamental group of a closed surface of genus at least 2? Many classes of groups have been shown to contain surface subgroups, but for some the answer is still unknown.I will present a family of 23 torsion free hyperbolic groups that act simply transitively on the vertices of hyperbolic triangular buildings of the smallest non-trivial thickness, and discuss the search for surface subgroups in these groups. The idea is to find periodic apartments using the combinatorics of the underlying geometry. The found periodic apartments then give rise to surface subgroups.
The search for periodic apartments giving genus 2 surface subgroups can be done with relatively simple algorithms, but for genera 3 and 4 expertise from computer scientists Savela, Oikarinen and Järvisalo was needed. They were able to perform exhaustive search for genus 3 using novel SAT encodings and a specialised orderly algorithm, and also for genus 4 with the aid of massive parallel computing. As a result seven groups have been shown to have surface subgroups, leaving 14 of the 23 groups for further inspection.
Based on joint work with Alina Vdovina, Jarkko Savela, Emilia Oikarinen, and Matti Järvisalo.
| Aikajakso | 19 elok. 2021 |
|---|---|
| Tapahtuman otsikko | Groups, Graphs, Geometry and Complexity 2021 |
| Tapahtuman tyyppi | Conference |
| Sijainti | Newcastle, Iso-BritanniaNäytä kartalla |
| Tunnustuksen arvo | International |