#### 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

Email: cohen@math.lsu.edu, gdenham@uwo.ca, a.suciu@neu.edu

URL:
http://www.math.lsu.edu/~cohen,
http://www.math.uwo.ca/~gdenham,
http://www.math.neu.edu/~suciu

AGT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**