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.

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