The bridge number of surface links and kei colorings

Abstract

Meier and Zupan introduced bridge trisections of surface links in S 4 $S^4$ as a 4-dimensional analogue to bridge decompositions of classical links, which gives a numerical invariant of surface links called the bridge number. We prove that there exist infinitely many surface knots with bridge number n $n$ for any integer n ⩾ 4 $n \geqslant 4$ . To prove it, we use colorings of surface links by keis and give lower bounds for the bridge number of surface links.