Counting Dirac braid relators and hyperelliptic Lefschetz fibrations
Abstract
We define a new invariant for hyperelliptic Lefschetz fibrations over closed oriented surfaces, which counts the number of Dirac braids included intrinsically in the monodromy, by using chart description introduced by the second author. As an application, we prove that two hyperelliptic Lefschetz fibrations of genus over a given base space are stably isomorphic if and only if they have the same numbers of singular fibers of each type and they have the same value of if is odd. We also give examples of pair of hyperelliptic Lefschetz fibrations with the same numbers of singular fibers of each type which are not stably isomorphic.
Keywords
Cite
@article{arxiv.1508.07687,
title = {Counting Dirac braid relators and hyperelliptic Lefschetz fibrations},
author = {Hisaaki Endo and Seiichi Kamada},
journal= {arXiv preprint arXiv:1508.07687},
year = {2017}
}
Comments
30 pages, 32 figures; (v2) the title changed, Section 1 rewritten, remarks added. arXiv admin note: text overlap with arXiv:1403.7946