The Levine-Tristram signature: a survey

Abstract

The Levine-Tristram signature associates to each oriented link $L$ in $S^3$ a function ${\sigma }_L:S^1\to \mathbb{Z}.$ 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.

18 pages