In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present formulation is closer in spirit to the usual TQFT framework, and allows a more direct comparison with Fukaya-categorical constructions. The result also leads to various dualities in bordered Floer homology.
Cite this article
Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston, Heegaard Floer homology as morphism spaces. Quantum Topol. 2 (2011), no. 4, pp. 381–449DOI 10.4171/QT/25