The Conley index, gauge theory, and triangulations

2013/08/29 by Ciprian Manolescu, Manolescu, Ciprian
Mathematics · #37B30 #57M27 (Secondary) #57Q15 #57R58 (Primary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1308.6366

openalex publication_date 2013/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The proximal-proximal gradient algorithm
• Suspensions of homology spheres
• Shrinking Cell-Like Decompositions of Manifolds. Codimension Three
• Periodic Floer pro-spectra from the Seiberg-Witten equations
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds

Related

• Lectures on the triangulation conjecture
• Polytopes, dualities, and Floer homology
• Floer theory and its topological applications
• Lectures on monopole Floer homology
• The Conley index for discrete dynamical systems and the mapping torus