Simple expressions for the holed torus relations

Abstract

In the mapping class group of a $k$-holed torus with $0\le k\le 9$, one can factorize the boundary multi-twist (or the identity when $k=0$) as the product of twelve right-handed Dehn twists. Such factorizations were explicitly given by Korkmaz and Ozbagci for each $k\le 9$ and an alternative one for $k=8$ by Tanaka. In this note, we simplify their expressions for the $k$-holed torus relations.

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References in corpus (1)

• Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus

Cited by in corpus (1)

• Sections of the Matsumoto-Cadavid-Korkmaz Lefschetz fibration