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Arbitrarily Long Factorizations in Mapping Class Groups
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Date
2015-01-01
Author
DALYAN, ELİF
Korkmaz, Mustafa
Pamuk, Mehmetcik
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On a compact oriented surface of genus g with n= 1 boundary components, d1, d2,..., dn, we consider positive factorizations of the boundary multitwist td1 td2 tdn, where tdi is the positive Dehn twist about the boundary di. We prove that for g= 3, the boundary multitwist td1 td2 can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn- Morris, who proved this result for g= 8. This fact has immediate corollaries on the Euler characteristics of the Stein fillings of contact three manifolds.
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URI
https://hdl.handle.net/11511/42182
Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
DOI
https://doi.org/10.1093/imrn/rnu226
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Department of Mathematics, Article
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E. DALYAN, M. Korkmaz, and M. Pamuk, “Arbitrarily Long Factorizations in Mapping Class Groups,”
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
, pp. 9400–9414, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42182.