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Meier and Zupan introduced bridge trisections of surface links in $S^4$ as a4-dimensional analogue to bridge decompositions of classical links, which givesa numerical invariant of surface links called the bridge number. We prove thatthere exist infinitely many surface knots with bridge number $n$ for anyinteger $n \geq 4$. To prove it, we use colorings of surface links by keis andgive lower bounds for the bridge number of surface links.

The bridge number of surface links and kei colorings