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HOMFLY Homology for Oriented Tangles
Geometry/Topology| Speaker: | Luke Conners, University of Zurich |
| Related Webpage: | https://sites.google.com/view/lukegconners/home |
| Location: | 2112 MSB |
| Start time: | Fri, Oct 23 2026, 11:00AM |
Description
We introduce an extension of Khovanov and Rozansky's categorification of the HOMFLY polynomial to oriented tangles. Unlike previous such extensions, ours is invariant under the full suite of oriented Reidemeister moves, including the "misoriented" Reidemeister IIb. For oriented links L, this removes the preliminary step of presenting L as a braid closure. Our construction admits an interpretation in terms of Bar-Natan's "canopoly" framework, allowing for local computations. Time permitting, we will briefly discuss potential consequences for functoriality under (non-compact) oriented tangle cobordisms and extracting smooth 4-manifold invariants. Based on forthcoming joint work with William Ballinger.