On the decategorification of Ozsváth and Szabó's bordered theory for knot Floer homology
Andrew Manion
University of Southern California, Los Angeles, USA
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Abstract
We relate decategorifications of Ozsváth–Szabó's new bordered theory for knot Floer homology to representations of . Specifically, we consider two subalgebras and of Ozsváth–Szabó's algebra , and identify their Grothendieck groups with tensor products of representations and of , where is the vector representation. We identify the decategorifications of Ozsváth–Szabó's bimodules for tangles with corresponding maps between representations. Finally, when the algebras are given multi-Alexander gradings, we demonstrate a relationship between the decategorification of Ozsváth–Szabó's theory and Viro's quantum relative of the Reshetikhin–Turaev functor based on .
Cite this article
Andrew Manion, On the decategorification of Ozsváth and Szabó's bordered theory for knot Floer homology. Quantum Topol. 10 (2019), no. 1, pp. 77–206
DOI 10.4171/QT/123