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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): Hisaaki Endo; Seiji Nagami
Journal: Trans. Amer. Math. Soc. 357 (2005), 3179-3199.
MSC (2000): Primary 57R20; Secondary 57N13, 20F05, 14D06
Posted: September 2, 2004
MathSciNet review: 2135741
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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 and which violate slope bounds for non-hyperelliptic fibrations on algebraic surfaces of general type.

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