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
Publication date:
29.9.2020.
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