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SUMMARY:Trivial braid detection via Khovanov homology - Eli Grigsby (Bosto
 n College)
DTSTART:20170118T113000Z
DTEND:20170118T123000Z
UID:TALK69996@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this 3-lecture series we will explore the many ways in whic
 h key&nbsp\;&nbsp\;<i>representation-theoretic</i>&nbsp\;features of the a
 nnular Khovanov-Lee homology of braid closures give information&nbsp\;abou
 t the&nbsp\;surfaces they bound in the 4-ball as well as&nbsp\;their dynam
 ics when viewed as mapping classes of the punctured disk.<br><br>In the fi
 rst lecture\, we will introduce Plamenevskaya&#39\;s transverse invariant 
 in Khovanov homology and show how it can be used to detect the trivial bra
 id (j. work with J. Baldwin). The proof uses fundamental properties of the
  left-invariant order on the braid group as well as&nbsp\;algebraic proper
 ties of the Khovanov complex of braid closures.<br>
LOCATION:Seminar Room 1\, Newton Institute
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