Mathematics Colloquia and Seminars

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We adapt work of Kirby-Thompson and Zupan to define an integer invariant $L(T)$ of a bridge trisection $T$ of a smooth surface $K$ in $S^4$ or $B^4$ . We show that when $L(T) = 0$, then the surface $K$ is unknotted. We also show show that for a trisection $T$ of an irreducible surface, bridge number produces a lower bound for $L(T)$. Consequently $L$ can be arbitrarily large.