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Reidemeister torsion,
peripheral complex and Alexander polynomials of hypersurface
complements
Yongqiang Liu and Laurenţiu Maxim |
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Algebraic & Geometric Topology 15 (2015) 2755–2785
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Abstract |
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Let be a polynomial that is transversal (or regular) at infinity. Let be the corresponding affine hypersurface complement. By using the peripheral complex associated to , we give several estimates for the (infinite cyclic) Alexander polynomials of induced by , and we describe the error terms for such estimates. The obtained polynomial identities can be further refined by using the Reidemeister torsion, generalizing a similar formula proved by Cogolludo and Florens in the case of plane curves. We also show that the above-mentioned peripheral complex underlies an algebraic mixed Hodge module. This fact allows us to construct mixed Hodge structures on the Alexander modules of the boundary manifold of . |
Keywords
Reidemeister torsion, Sabbah specialization complex, nearby
cycles, peripheral complex, hypersurface complement, Milnor
fibre, non-isolated singularities, Alexander polynomial,
boundary manifold, mixed Hodge structure
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Mathematical Subject Classification 2010
Primary: 32S25
Secondary: 32S55, 32S60
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References |
Publication
Received: 13 June 2014
Accepted: 13 February 2015
Published: 10 December 2015
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Authors |
| Yongqiang Liu | |
| School of Mathematical
Sciences University of Science and Technology of China No 96, JinZhai Road Hefei, 230026 China |
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| http://home.ustc.edu.cn/~liuyq/ | |
| Laurenţiu Maxim | |
| Department of Mathematics University of Wisconsin–Madison 480 Lincoln Drive Office 713 Madison, WI 53706-1388 USA |
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| http://www.math.wisc.edu/~maxim/ | |
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