Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations

Endo, Hisaaki; Nagami, Seiji

doi:10.1090/S0002-9947-04-03643-8

Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations
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by Hisaaki Endo and Seiji Nagami PDF

Trans. Amer. Math. Soc. 357 (2005), 3179-3199 Request permission

Abstract:

We introduce the notion of signature for relations in mapping class groups and show that the signature of a Lefschetz fibration over the 2-sphere is the sum of the signatures for basic relations contained in its monodromy. Combining explicit calculations of the signature cocycle with a technique of substituting positive relations, we give some new examples of non-holomorphic Lefschetz fibrations of genus $3, 4$ and $5$ which violate slope bounds for non-hyperelliptic fibrations on algebraic surfaces of general type.

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