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

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.02171
 arXiv:
 arXiv:1701.02171
 Bibcode:
 2017arXiv170102171H
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Symplectic Geometry;
 57M50;
 57R17
 EPrint:
 This note has been integrated into a larger article project