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Trivial braid detection via Khovanov homology

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HTLW01 - Winter school workshop

In this 3-lecture series we will explore the many ways in which key  representation-theoretic features of the annular Khovanov-Lee homology of braid closures give information about the surfaces they bound in the 4-ball as well as their dynamics when viewed as mapping classes of the punctured disk.

In the first lecture, we will introduce Plamenevskaya's transverse invariant in Khovanov homology and show how it can be used to detect the trivial braid (j. work with J. Baldwin). The proof uses fundamental properties of the left-invariant order on the braid group as well as algebraic properties of the Khovanov complex of braid closures.

This talk is part of the Isaac Newton Institute Seminar Series series.

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