Subgroups of the Torelli group generated by two symmetric bounding pair maps

Kodai Mathematical Journal

Michał Stukow¹ 

[1] Institute of Mathematics Faculty of Mathematics Physics and Informatics University of Gdańsk

关键词: Mapping class group;    Torelli group;    Free group;    Bounding pair map;   

DOI  :  10.2996/kmj/1478073770

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(9)Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group. This supports the conjecture stated by C. Leininger and D. Margalit that any pair of elements of the Torelli group either commute or generate a free group.

【 授权许可】

Unknown