Lectures on monopole Floer homology

Abstract

These lecture notes are a friendly introduction to monopole Floer homology. We discuss the relevant differential geometry and Morse theory involved in the definition. After developing the relation with the four-dimensional theory, our attention shifts to gradings and correction terms. Finally, we sketch the analogue in this setup of Manolescu's recent disproof of the long standing Triangulation Conjecture.

arXiv comment37 pages, 5 pictures. To appear in the Proceedings of the 22nd Gökova Geometry/Topology Conference

References in corpus (3)

• Circle-valued Morse theory and Reidemeister torsion
• Monopole Floer homology for rational homology 3-spheres
• Lectures on the triangulation conjecture

Cited by in corpus (5)

• The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds
• Manolescu correction terms and knots in the three-sphere
• Khovanov homology in characteristic two and involutive monopole Floer homology
• Monopole Floer homology and SOLV geometry
• Non-formality in $\mathrm{Pin}(2)$-monopole Floer homology