Algebraic and Geometric Topology 3 (2003), paper no. 16, pages 511-535.

Torsion in Milnor fiber homology

Daniel C. Cohen, Graham Denham, Alexander I. Suciu

Abstract. In a recent paper, Dimca and Némethi pose the problem of finding a homogeneous polynomial f such that the homology of the complement of the hypersurface defined by f is torsion-free, but the homology of the Milnor fiber of f has torsion. We prove that this is indeed possible, and show by construction that, for each prime p, there is a polynomial with p-torsion in the homology of the Milnor fiber. The techniques make use of properties of characteristic varieties of hyperplane arrangements.

Keywords. Milnor fibration, characteristic variety, arrangement

AMS subject classification. Primary: 32S55. Secondary: 14J70, 32S22, 55N25.

DOI: 10.2140/agt.2003.3.511

E-print: arXiv:math.GT/0302143

Submitted: 14 February 2003. Accepted: 19 May 2003. Published: 15 June 2003.

Notes on file formats

Daniel C. Cohen, Graham Denham, Alexander I. Suciu

Department of Mathematics, Louisiana State University
Baton Rouge, LA 70803, USA

Department of Mathematics, University of Western Ontario
London, ON N6A 5B7, Canada

Department of Mathematics, Northeastern University, Boston, MA 02115, USA


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