Topology Seminar: Liam Watson (UCLA), 'Khovanov homology, tangles, and strong inversions'

Event Date: 

Tuesday, May 14, 2013 -
3:30pm to 4:30pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Daryl Cooper

Email: cooper@math.ucsb.edu

Abstract: A knot $K$ is strongly invertible if there is an orientation preserving involution $f$ on $S^3$ that reverses orientation on $K$. The pair $(K,f)$ gives rise to a tangle, the two-fold branch cover of which is the exterior of $K$. This talk will focus on tangles of this form, and in particular, introduce an invariant of tangles extracted from Khovanov homology. This object may be viewed as an invariant of the pair $(K,f)$; our observation is that different strong inversions (as elements of the symmetry group of the knot) are often distinguished by this invariant.