Floer homology of Lagrangians in clean intersection

TL;DR

This paper develops spectral sequences based on Morse-Bott Floer homology to compute Floer homology for pairs of monotone, cleanly intersecting Lagrangian submanifolds, including a comprehensive treatment of orientations.

Contribution

It introduces two spectral sequences for Floer homology in the clean intersection case, extending Morse-Bott Floer homology with a complete orientation framework.

Findings

Spectral sequences facilitate Floer homology calculations for clean intersections.

The theory includes a detailed orientation treatment.

Provides tools for explicit Floer homology computations in specific cases.

Abstract

We consider Floer homology associated to a pair of closed Lagrangian submanifolds that satisfy a monotonicty assumption. If the Lagrangians intersect cleanly we decribe two spectral sequences which help to compute their Floer homology. The spectral sequences are constructed using a Morse-Bott version of Floer homology. We give a full treatment of the theory including orientations.