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 link in the 3-sphere. As a corollary, we construct bilinear forms on the twisted Alexander modules of links.
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Notes
See [3, Sects. 1–2 ] for details.
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Acknowledgements
The author sincerely expresses his gratitude to Akio Kawauchi for many useful discussions on the classical Blanchfield pairing. He also thanks Takahiro Kitayama and Masahico Saito for valuable comments. The work is partially supported by JSPS KAKENHI Grant Number 00646903.
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Nosaka, T. Twisted cohomology pairings of knots I; diagrammatic computation. Geom Dedicata 189, 139–160 (2017). https://doi.org/10.1007/s10711-017-0221-5
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DOI: https://doi.org/10.1007/s10711-017-0221-5