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A presentation for the mapping class group of the closed non-orientable surface of genus 4. (English) Zbl 1182.57016
Though it is known in principle that the mapping class groups of all closed surfaces are finitely presented, explicit finite presentations have proved difficult to calculate for the nonorientable surfaces. The author, who previously had given a general method for finding such presentations, provides here an explicit finite presentation for the mapping class group of the closed nonorientable surface of genus 4.
The author states, “The set of generators in this presentation consists of 5 Dehn twists, 3 crosscap transpositions and one involution, and it can be immediately reduced to the generating set found by D. R. J. Chillingworth [Proc. Camb. Philos. Soc. 65, 409–430 (1969; Zbl 0172.48801)].”
The method employed in finding the presentation considers the action of the group on the ordered complex of curves.

MSC:
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
20F05 Generators, relations, and presentations of groups
20F38 Other groups related to topology or analysis
57M99 General low-dimensional topology
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References:
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