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Organizers |
On categorical traces and homology for links in a solid torus
by
Krzysztof K Putyra
ETHZ Institute for Theoretical Studies
Coauthors: Anna Beliakova
A trace of a category is the set of its endomorphisms considered up to conjugation. For example, the trace of the category of tangles is the set of links in a solid torus: every such a link is a closure of a tangle and closures of two tangles coincide if and only if the tangles agree up to conjugation. The categorical trace is functorial: a functor between categories induces a map between their traces. In particular, we can obtain invariants of links in a solid torus from functors on the category of tangles. In my talk I will discuss the trace of the tangle invariant due to Chen and Khovanov, which recovers the annular sl2 homology defined by Asaeda, Przytycki, and Sikora. This construction almost immediately equips the APS homology with an action of sl2. With a small modification of the trace construction one can quantize the homology to obtain a sequence of representations of quantum sl2.
Date received: November 3, 2015
Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-22.