Charts, signatures, and stabilizations of Lefschetz fibrations
arXiv:1403.7946
Abstract
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.
arXiv comment30 pages, 29 figures; (v2) a co-author added; (v3) proofs simplified, remarks and references added, typos corrected; (v4) symbols simplified, examples added, typos corrected
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