Algebraic Graph Theory International Webinar (1.2.2022)
v utorok 1.2.2022 o 19:00 hod.
Od: Róbert Jajcay
The organizers of the Algebraic Graph Theory International Webinar would like to invite you to join us and other colleagues on Februar 1, 2022, at 7pm Central European Summer Time (= 6pm UTC), for the next presentation delivered by Roman Nedela.
The title of Martin's talk: On equivalence of discrete groups
Let S be an orientable surface of genus g. Denote by Hom+(S) its group of orientation-preserving homeomorphisms. We say that a finite group G acts on S if there is monomorphism e: G -> Hom+(S). Every action may be constructed by means of a pair of Fuchsian groups K < Gamma < PSL(2,R) acting discontinuosly on the upper half plane U and an epimorphism f: Gamma -> G with kernel K, where K is a surface group. Such an epimorphism will be called order preserving . The epimorphism f is constructed from e and a homeomorphism U/K cong S. Two such actions are equivalent if and only if there is an automorphism a in Aut+(Gamma) and an automorphism b in Aut(G) such that the respective order preserving epimorphisms satisfy the relation e'=b(e a).
In my talk I will discuss the problem of determining of equivalence classes of discrete actions. In particular, we investigate the action of Aut+(Gamma) on the set of epimorphisms Epi(Gamma,G) for a finite group G and a Fuchsian group Gamma. In case of planar Fuchsian groups, that means groups with signature (0;m_1,...,m_r), we present a complete answer giving rise to an algorithm constructing the equivalence classes. I present a list of such actions of small genera. In the general case, we have a partial result.
Joint work with M. Skyvova and J. Karabas.
The Zoom link for this semester is:
Meeting ID: 871 9332 0713
Further details may be found at http://euler.doa.fmph.uniba.sk/AGTIW.html
where you can also find the slides and the recordings of our previous presentations. Also, if you wish to advertise an AGT friendly conference on this page, please send us the link.
Hoping to see you at the webinar, and wishing you all the best.