Twisted torsion invariants and link concordance

Details Twisted torsion invariants and link concordance Twisted torsion invariants and link concordance

2010-01-06

arxiv.org/abs/1001.0926v2

Mathematics

Geometric Topology

24 pages, 1 figure. Expositions improved

Scientific paper

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. 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 eight knot is not slice.

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