Gauge Theory and Topology: The annular Bar-Natan category and handle-slides

Gauge Theory and Topology Seminar, SEMINARS

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March 3, 2023 3:30 pm - 4:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Matthew Hogancamp - Northeastern University

Khovanov homology can be upgraded to an invariant of pairs (K,V) where K is a framed knot and V is an object of the annular Bar-Natan category (ABN). In this context, the pair (K,V) is called a colored knot, and its Khovanov invariant is called colored Khovanov homology.  In my talk I will discuss recent joint work with David Rose and Paul Wedrich, in which we construct an object in ABN (more accurately, an ind-object therein), called a Kirby color, whose associated colored Khovanov invariant satisfies the important handle-slide relation.  Our work gives an annular perspective on the Manolescu-Neithalath 2-handle formula for sl(2) skein lasagna modules.