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Torsion in Milnor fiber homology

Daniel C Cohen, Graham Denham and Alexander I Suciu

Algebraic & Geometric Topology 3 (2003) 511–535

arXiv: math.GT/0302143


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.

Milnor fibration, characteristic variety, arrangement
Mathematical Subject Classification 2000
Primary: 32S55
Secondary: 14J70, 32S22, 55N25
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Received: 14 February 2003
Accepted: 19 May 2003
Published: 15 June 2003
Daniel C Cohen
Department of Mathematics
Louisiana State University
Baton Rouge LA 70803
Graham Denham
Department of Mathematics
University of Western Ontario
London, ON N6A 5B7
Alexander I Suciu
Department of Mathematics
Northeastern University
Boston MA 02115