Algebraic Graph Theory Seminar - Ján Karabáš (9.4.2021)
Friday 9.4.2021 at 13:00, online
By: Martin Mačaj
Ján Karabáš (Matej Bel University in Banska Bystrica):
Classification of finite group actions on orientable surfaces of low genera
The problem of classifying all finite group actions on orientable surfaces of low genera is considered. Our aim is to extend the existing classifications (genera 2 and 3 by Broughton (1990), genus 4 by Bogopolsky (1991) and genus 5 by Kuribayashi and Kimura (1990)) to higher genera using computer algebra systems. On the other hand, Marston Conder classified actions of all “large groups” on orientable surfaces of genera up to 101 (late 2000’s). The latter catalogue is not satisfactory because of two reasons: 1. The groups considered in Conder’s list have orders at least , given genus , and 2. The equivalence of the group actions on Conder’s list is different of the equivalence considered in earlier works.
We will mainly discuss the problem of transferring (so-called) topological equivalence of actions into purely algebraic form and further, the problem of implementation of such test. As follows, the problem of equivalence of group actions involves (at least partial) knowledge of group of automorphisms of given Fuchsian group — a deep and interesting problem itself.
(a joint work with Roman Nedela and Mária Skyvová, University of West Bohemia in Pilsen)
Due to recent restrictions imposed on us in response to the worsening of the situation with Covid infections in Slovakia, we will switch to distance mode. You will receive an MS Teams link over which you will be able to follow the presentation, ask questions, comment, and possibly even offer some solutions. While it is not better than being personally in the lecture room, it is not a terrible way to keep in touch either. Let us hope that we will soon be able to attend the meetings in person.