The Levine-Tristram signature: a survey

11 Mar 2019  ·  Conway Anthony ·

The Levine-Tristram signature associates to each oriented link $L$ in $S^3$ a function $\sigma_L \colon S^1 \to \mathbb{Z}.$ This invariant can be defined in a variety of ways, and its numerous applications include the study of unlinking numbers and link concordance. In this survey, we recall the three and four dimensional definitions of $\sigma_L$, list its main properties and applications, and give comprehensive references for the proofs of these statements...

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Geometric Topology