We show that for a tangle with the Hochschild homology of the tangle Floer homology is equivalent to the link Floer homology of the closure of the tangle, linked with the tangle axis. In addition, we show that the action of the braid group on tangle Floer homology is faithful.
"A self-pairing theorem for tangle Floer homology." Algebr. Geom. Topol. 16 (4) 2127 - 2141, 2016. https://doi.org/10.2140/agt.2016.16.2127