The signature of positive braids is linearly bounded by their first Betti number

Abstract

We provide linear lower bounds for the signature of positive braids in terms of the three genus of their braid closure. This yields linear bounds for the topological slice genus of knots that arise as closures of positive braids.

14 pages, 2 figures. Version 2: Change of sign convention for the signature of links, minor corrections, implementation of referee's recommendations

References in corpus (1)

• The volume of positive braid links

Cited by in corpus (2)

• A sharp signature bound for positive four-braids
• Signature and concordance of positive knots