Title: A bordered monopole Floer theory

Abstract: I'll discuss work-in-progress toward constructing monopole Floer 
theoretic invariants of bordered 3-manifolds. Roughly, our construction 
associates an A-infinity algebra to a surface, an A-infinity module to a 
bordered 3-manifold, and a map of A-infinity modules to a 4-dimensional 
cobordism of bordered 3-manifolds. I'll focus on the topological and 
algebraic aspects of our work and, in particular, will indicate how we 
prove a pairing theorem relating the invariants of two bordered 
3-manifolds with that of the manifold obtained by gluing the former 
together along homeomorphic components of their boundaries. This is joint 
work with Jon Bloom.