Generating the mapping class group of a nonorientable surface by three torsions

被引:1
|
作者
Lesniak, Marta [1 ]
Szepietowski, Blazej [1 ]
机构
[1] Univ Gdansk, Fac Math Phys & Informat, Inst Math, PL-80308 Gdansk, Poland
关键词
Mapping class group; Nonorientable surface; Torsion generators; TWIST SUBGROUP; ELEMENTS; SPACE;
D O I
10.1007/s10711-022-00698-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that the mapping class group M (N-g) of a closed nonorientable surface of genus g different than 4 is generated by three torsion elements. Moreover, for every even integer k >= 12 and g of the form g = pk + 2q(k - 1) or g = pk + 2q(k - 1) + 1, where p, q are non-negative integers and p is odd, M (N-g) is generated by three conjugate elements of order k. Analogous results are proved for the subgroup of M (N-g) generated by Dehn twists.
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页数:14
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