A Floer-Gysin exact sequence for Lagrangian submanifolds

TL;DR

This paper develops a Floer-theoretical analog of the classical Gysin sequence, enabling new computations and insights into the topology of Lagrangian submanifolds within symplectic geometry.

Contribution

It introduces a novel Floer-Gysin exact sequence for Lagrangian submanifolds, extending classical topological tools to Floer theory.

Findings

Derived applications to Lagrangian Floer homology computations

Analyzed algebraic and functorial properties of the sequence

Provided new topological insights into Lagrangian submanifolds

Abstract

In this paper we establish a Floer-theoretical analog of the classical Gysin long exact sequence from algebraic topology for circle bundles. We study algebraic and functorial properties of this sequence and derive applications to computations of Lagrangian Floer homologies as well as to questions on the topology of Lagrangian submanifolds.