A presentation for the mapping class group of the closed non-orientable surface of genus 4

Abstract

Finite presentations for the mapping class group M(F) are known for arbitrary orientable compact surface F. If F is non-orientable, then such presentations are known only when F has genus at most 3 and few boundary components. In this paper we obtain finite presentation for the mapping class group of the closed non-orientable surface of genus 4 from its action on the so called ordered complex of curves.

28 pages, 7 figures

References in corpus (2)

• Dehn twists on nonorientable surfaces
• Generating mapping class groups of nonorientable surfaces with boundary

Cited by in corpus (10)

• A finite presentation for the mapping class group of a nonorientable surface with Dehn twists and one crosscap slide as generators
• Crosscap slides and the level 2 mapping class group of a nonorientable surface
• A presentation for the mapping class group of a nonorientable surface
• Low dimensional linear representations of the mapping class group of a nonorientable surface
• The twist subgroup of the mapping class group of a nonorientable surface
• A normal generating set for the Torelli group of a non-orientable closed surface
• An infinite presentation for the twist subgroup of the mapping class group of a compact non-orientable surface
• A normal generating set for the Torelli group of a compact non-orientable surface
• Generating the mapping class group of a nonorientable surface by crosscap transpositions
• Outer Automorphisms of Mapping Class Groups of Nonorientable Surfaces