Generating the mapping class group of a nonorientable surface by crosscap transpositions

Marta Leśniak , Błażej Szepietowski

Abstract

A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two crosscaps. We prove that the mapping class group of a compact nonorientable surface of genus is generated by conjugates of one crosscap transposition. In the case when the surface is either closed or has one boundary component, we give an explicit set of crosscap transpositions generating the mapping class group.
Author Marta Leśniak IM
Marta Leśniak,,
- Institute of Mathematics
, Błażej Szepietowski IM
Błażej Szepietowski,,
- Institute of Mathematics
Journal seriesTopology and Its Applications, ISSN 0166-8641
Issue year2017
Vol229
Pages20-26
Publication size in sheets0.5
Keywords in Englishmapping class group, nonorientable surface, crosscap transposition
DOIDOI:10.1016/j.topol.2017.07.006
URL https://doi.org/10.1016/j.topol.2017.07.006
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 20.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.377 (2) - 2016=0.464 (5)
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