Volume 11, issue 1 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The Meyer functions for projective varieties and their application to local signatures for fibered $4$–manifolds

Yusuke Kuno

Algebraic & Geometric Topology 11 (2011) 145–195
Abstract

We study a secondary invariant, called the Meyer function, on the fundamental group of the complement of the dual variety of a smooth projective variety. This invariant has played an important role when studying the local signatures of fibered 4–manifolds from topological point of view. As an application of our study, we define a local signature for generic nonhyperelliptic fibrations of genus 4 and 5 and compute some examples.

Keywords
mapping class group, Meyer function, bounded cohomology, local signature
Mathematical Subject Classification 2000
Primary: 14D05, 57N13
References
Publication
Received: 6 May 2010
Revised: 2 October 2010
Accepted: 13 October 2010
Published: 6 January 2011
Authors
Yusuke Kuno
Department of Mathematics
Graduate School of Science
Hiroshima University
1-3-1 Kagamiyama
Higashi-Hiroshima
739-8526
Japan