Original scientific paper

A note on the curve complex of the 3-holed projective plane

Blazej Szepietowski orcid.org/0000-0002-6219-7895 ; Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdansk, Gdansk, Poland

Abstract

Let S be a projective plane with 3 holes. We prove that there is an exhaustion of the curve complex C(S) by a sequence of finite rigid sets. As a corollary, we obtain that the group of simplicial automorphisms of C(S) is isomorphic to the mapping class group Mod(S). We also prove that C(S) is quasi-isometric to a simplicial tree.

Keywords

Complex of curves, nonorientable surface, projective plane, mapping class group, quasi-tree

Hrčak ID:

244289

URI

https://hrcak.srce.hr/244289

Publication date:

29.9.2020.

Visits: 827 *