Georgia Institute of Technology College of Sciences

A contact manifold with boundary naturally gives rise to a sutured manifold, as defined by Gabai. Honda, Kazez and Matic have used this relationship to define an invariant of contact manifolds with boundary in sutured Floer homology, a Heegaard-Floer-type invariant of sutured manifolds developed by Juhasz. More recently, Kronheimer and Mrowka have defined an invariant of sutured manifolds in the setting of monopole Floer homology. In this talk, I'll describe work-in-progress to define an invariant of contact manifolds with boundary in their sutured monopole theory. If time permits, I'll talk about analogues of Juhasz' sutured cobordism maps and the Honda-Kazez-Matic gluing maps in the monopole setting. Likely applications of this work include an obstruction to the existence of Lagrangian cobordisms between Legendrian knots in S^3. Other potential applications include the construction of a bordered monopole theory, following an outline of Zarev. This is joint work with Steven Sivek.