Hisaaki Endo, Isao Hasegawa, Seiichi Kamada, Kokoro Tanaka
Published 2014-03-31, updated 2015-02-15Version 4
We employ a certain labeled finite graph, called a chart, in a closed oriented surface for describing the monodromy of a(n achiral) Lefschetz fibration over the surface. Applying charts and their moves with respect to Wajnryb's presentation of mapping class groups, we first generalize a signature formula for Lefschetz fibrations over the 2-sphere obtained by Endo and Nagami to that for Lefschetz fibrations over arbitrary closed oriented surface. We then show two theorems on stabilization of Lefschetz fibrations under fiber summing with copies of a typical Lefschetz fibration as generalizations of a theorem of Auroux.
Comments: 30 pages, 29 figures; (v2) a co-author added; (v3) proofs simplified, remarks and references added, typos corrected; (v4) symbols simplified, examples added, typos corrected
Stabilization for mapping class groups of 3-manifolds
Abelian subgroups of the mapping class groups for non-orientable surfaces
Matrix Group Integrals, Surfaces, and Mapping Class Groups II: $\mathrm{O}\left(n\right)$ and $\mathrm{Sp}\left(n\right)$
![QR code for arXiv:1403.7946 [math.GT]](http://oss.arxitics.com/images/favicon.svg)