Twisted cohomology pairings of knots I; diagrammatic computation

Nosaka, Takefumi

doi:10.48550/arxiv.1602.01129

2016

DOI: 10.48550/arxiv.1602.01129

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Twisted cohomology pairings of knots I; diagrammatic computation

Takefumi Nosaka

Abstract: We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a corollary, we construct bilinear forms on the twisted Alexander modules of links.

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Cited by 2 publications

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Bilinear-form invariants of Lefschetz fibrations over the 2-sphere

Nosaka¹

2016

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We introduce invariants of, in general, Hurwitz equivalence classes with respect to arbitrary group G. The invariants are constructed from any right G-modules M and any G-invariant bilinear function on M , and are of bilinear forms. For instance, when G is the mapping class group of the closed surface, Mg, we get an invariant of 4-dimensional Lefschetz fibrations over the 2-sphere. Moreover, the construction is applicable for the quantum representations of Mg derived from Chern-Simons field theory. We also see that our invariant is unstable with respect to fiber sum of Lefschetz fibrations.

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Bilinear-form invariants of Lefschetz fibrations over the 2-sphere

Nosaka¹

2016

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Some comparisons of Blanchfield pairings and cohomology pairings of knots

Nosaka

2020

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Twisted cohomology pairings of knots I; diagrammatic computation

Cited by 2 publications

References 17 publications

Bilinear-form invariants of Lefschetz fibrations over the 2-sphere

Bilinear-form invariants of Lefschetz fibrations over the 2-sphere

Some comparisons of Blanchfield pairings and cohomology pairings of knots

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