Exact triangles in Seiberg-Witten Floer theory. Part III: proof of exactness

TL;DR

This paper proves the exactness of a sequence in Seiberg-Witten Floer theory by constructing chain homomorphisms, advancing the understanding of the algebraic structures underlying the theory.

Contribution

It provides a rigorous proof of exactness in Seiberg-Witten Floer theory's exact triangles through explicit chain homomorphisms.

Findings

Established the exactness of the sequence in the theory.

Constructed explicit chain homomorphisms.

Enhanced the algebraic framework of Seiberg-Witten Floer theory.

Abstract

This is the third part of the work on the exact triangles. We construct chain homomorphisms and show exactness of the resulting sequence.