Exact triangles in Seiberg-Witten Floer theory. Part II: geometric limits of flow lines

TL;DR

This paper advances the understanding of Seiberg-Witten Floer theory by analyzing how flow lines behave under manifold splitting, crucial for establishing exact triangles in the theory.

Contribution

It provides a detailed analysis of the splitting and gluing of flow lines in Seiberg-Witten Floer theory when a three-manifold is split along a torus.

Findings

Flow lines can be split and glued along tori in three-manifolds.

The analysis supports the construction of exact triangles in Floer homology.

The work completes the proof of exact triangles in the second part of the series.

Abstract

This is the second part of the proof of the exact traiangles in Seiberg-Witten Floer theory. We analyse the splitting and gluing of flow lines of the Chern-Simons-Dirac functional when the underlying three-manifold splits along a torus. (two corrections added)