SMS scnews item created by Catherine Meister at Mon 18 May 2026 1041
Type: Seminar
Distribution: World
Expiry: 1 Jun 2026
Calendar1: 20 May 2026 1200-1300
CalLoc1: SMRI Seminar Room (A12 Macleay Room 301)
CalTitle1: Constructing Symmetric Triangulations of Closed Manifolds
Auth: cmeister@ac02gr132pn7c.shared.sydney.edu.au (cmei0631) in SMS-SAML

Australian Geometric Topology Webinar: Akpanya

Constructing Symmetric Triangulations of Closed Manifolds

Reymond Akpanya, University of Sydney

Australian Geometric Topology Webinar, Wednesday 20th May 2026, 12 pm – 1 pm, SMRI Seminar Room (A12 Macleay Room 301), also on Zoom

Abstract: In this talk, we study simplicial triangulations of closed d-manifolds for d = 2, 3. Our focus lies on facet-transitive triangulations. Here, we call such a triangulation facet-transitive, if its automorphism group acts transitively on the corresponding facets. In this setting, the combinatorial structure of a facet-transitive triangulation is completely encoded by its automorphism group. For d=2, we use this fact and show that there are exactly 13 distinct types of facet-transitive triangulations, classified according to the action of the automorphism group on the triangulation. By exploiting this classification, we construct a census of 2-dimensional face-transitive triangulations with up to 1280 facets, comprising exactly 86802 facet-transitive triangulations. The construction is based on a correspondence between facet-transitive triangulations and vertex-transitive cubic graphs equipped with cycle double covers. Our goal is to obtain an analogous database in dimension 3 using a similar approach. This is ongoing joint work with Jonathan Spreer (USyd) and James Morgan (USyd).