Monotone Lagrangian Floer theory in smooth divisor complements: III

Abstract

This is the third paper in a series of papers studying intersection Floer theory of Lagrangians in the complement of a smooth divisor. We complete the construction of Floer homology for such Lagrangians.

56 pages, 8 figures. This paper is born out of the revisions of 1808.08915 and 1809.03409, where some parts of the older versions of 1808.08915 and 1809.03409 are moved here. We also added a brief speculative discussion at the end about a generalization of our construction to the case of non-compact Lagrangians and its formal similarity to the definition of monopole Floer homology