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Twisted Alexander invariants of complex hypersurface complements

Part of: Homology and cohomology theories Singularities Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  22 April 2018

Laurenţiu Maxim  and
Kaiho Tommy Wong
Laurenţiu Maxim
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA (maxim@math.wisc.edu; wong@math.wisc.edu)
Kaiho Tommy Wong
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA (maxim@math.wisc.edu; wong@math.wisc.edu)
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Abstract

We define and study twisted Alexander-type invariants of complex hypersurface complements. We investigate torsion properties for the twisted Alexander modules and extend the local-to-global divisibility results of Maxim and of Dimca and Libgober to the twisted setting. In the process, we also study the splitting fields containing the roots of the corresponding twisted Alexander polynomials.

Keywords

twisted Alexander polynomialtwisted Alexander modulecomplex hypersurfacesingularitiesHopf link

MSC classification

Primary: 32S20: Global theory of singularities; cohomological properties 32S25: Surface and hypersurface singularities 32S55: Milnor fibration; relations with knot theory 14J70: Hypersurfaces
Secondary: 32S60: Stratifications; constructible sheaves; intersection cohomology 55N25: Homology with local coefficients, equivariant cohomology
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 5 , October 2018 , pp. 1049 - 1073
Copyright
Copyright © Royal Society of Edinburgh 2018 

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