Pure Maths Colloquium: Contact structures, instantons, and Floer homology
30 October 2017 16:00 in CM221
Instanton homology was developed by Floer in the 1980s as a powerful invariant of 3-manifolds. In recent years, it has had some striking applications in low-dimensional topology which were inspired by newer, more accessible relatives such as Heegaard Floer homology. I will describe some joint work with John Baldwin along these lines, in which we use invariants of contact structures on 3-manifolds to study the fundamental groups of 3-manifolds which bound Stein surfaces, and to prove that a knot invariant called Khovanov homology detects the trefoil.
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