Subgroups of the Torelli group generated by two symmetric bounding pair maps
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Publication:502118
DOI10.2996/KMJ/1478073770zbMATH Open1355.57022arXiv1604.04833OpenAlexW2963743162MaRDI QIDQ502118
Publication date: 30 December 2016
Published in: Kodai Mathematical Journal (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1604.04833
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