The Conley index, gauge theory, and triangulations

TL;DR

This paper explains the construction of Seiberg-Witten Floer stable homotopy types using the Conley index and finite dimensional approximation, and discusses applications such as disproving the high-dimensional triangulation conjecture.

Contribution

It provides an exposition of the construction of Floer stable homotopy types and demonstrates their application in topological conjecture disproofs.

Findings

Disproof of the high-dimensional triangulation conjecture

Construction of Seiberg-Witten Floer stable homotopy types

Application of the Conley index in Floer theory

Abstract

This is an expository paper about Seiberg-Witten Floer stable homotopy types. We outline their construction, which is based on the Conley index and finite dimensional approximation. We then describe several applications, including the disproof of the high-dimensional triangulation conjecture.