Multivariable signatures, genus bounds and $0.5$-solvable cobordisms

Anthony Conway; Matthias Nagel; Enrico Toffoli

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arXiv · 1703.07540

Multivariable signatures, genus bounds and $0.5$-solvable cobordisms

Anthony Conway·Matthias Nagel·Enrico Toffoli

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Abstract

We refine prior bounds on how the multivariable signature and the nullity of a link change under link cobordisms. The formula generalizes a series of results about the 4-genus having their origins in the Murasugi-Tristram inequality, and at the same time extends previously known results about concordance invariance of the signature to a bigger set of allowed variables. Finally, we show that the multivariable signature and nullity are also invariant under $0.5$-solvable cobordism.

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Anthony Conway, Matthias Nagel, Enrico Toffoli. 2017-03-22. Multivariable signatures, genus bounds and $0.5$-solvable cobordisms. https://arxiv.org/abs/1703.07540

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