# Michael Abel : HOMFLY-PT homology of general link diagrams and its decategorification

In the construction of HOMFLY-PT homology, one must start with a link presented as a braid closure. This restriction was expected by Khovanov and Rozansky to be required for the homology to be an isotopy invariant. In this talk, after reviewing the construction of the HOMFLY-PT polynomial and homology, we explore the consequences of dropping this requirement and allowing general link diagrams. We explicitly show that the Reidemeister IIb move (where the strands have opposite orientations) fails. Finally we will show that the Euler characteristic of this homology theory is a deformed version of the HOMFLY-PT polynomial which detects "braidlike" isotopy of tangles and links. This new polynomial agrees with the HOMFLY-PT polynomial on link diagrams which are presented as closed braid diagrams.

**Category**: Geometry and Topology**Duration**: 01:34:48**Date**: April 19, 2016 at 4:25 PM**Views**: 133-
**Tags:**seminar, Geometry/topology Seminar

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