Lectures on the triangulation conjecture

2016/07/27 by Manolescu, Ciprian
#57M27 (Secondary) #57Q15 #57R58 (Primary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1607.08163

Abstract

We outline the proof that non-triangulable manifolds exist in any dimension greater than four. The arguments involve homology cobordism invariants coming from the Pin(2) symmetry of the Seiberg-Witten equations. We also explore a related construction, of an involutive version of Heegaard Floer homology.

Related

• Homology cobordism and triangulations
• Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
• Floer theory and its topological applications
• A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture
• Functions on surfaces and constructions of manifolds in dimensions three, four and five