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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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1435-5337
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Volume 25, Issue 3

Issues

Twisted torsion invariants and link concordance

Jae Choon Cha
  • Department of Mathematics and PMI, POSTECH, Pohang 790–784, Republic of Korea, and Korea Institute for Advanced Study, Seoul 130–722, Republic of Korea
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/ Stefan Friedl
Published Online: 2013-05-02 | DOI: https://doi.org/10.1515/form.2011.125

Abstract.

The twisted torsion of a 3-manifold is well known to be zero whenever the corresponding twisted Alexander module is non-torsion. Under mild extra assumptions we introduce a new twisted torsion invariant which is always non-zero. We show how this torsion invariant relates to the twisted intersection form of a bounding 4-manifold, generalizing a theorem of Milnor to the non-acyclic case. Using this result, we give new obstructions to 3-manifolds being homology cobordant and to links being concordant. These obstructions are sufficiently strong to detect that the Bing double of the Figure 8 knot is not slice.

Keywords: Twisted torsion; homology cobordism; link concordance

About the article

Received: 2010-09-30

Revised: 2011-03-19

Published Online: 2013-05-02

Published in Print: 2013-05-01


Citation Information: Forum Mathematicum, Volume 25, Issue 3, Pages 471–504, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.125.

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