Gauge Theory and Topology: Monopoles and families of contact structures

Gauge Theory and Topology Seminar, SEMINARS

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November 18, 2022 3:30 pm - 4:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Juan Muñoz-Echániz - Columbia University

Beyond the tight/overtwisted dichotomy, 3-dimensional contact topology would appear to be dominated by flexibility: a central result of Eliashberg and Mishachev says that the contactomorphism group of the standard contact 3-ball has the homotopy type of the diffeomorphism group. In contrast with this, I will discuss how monopole Floer homology imposes constraints on the behaviour of families of contact structures on 3-manifolds. Applications include detecting exotic contactomorphisms given by certain "Dehn twists" on embedded spheres.