Title: Bordered Floer homology and splicing knot complements

Abstract: We use bordered Floer homology to study 3-manifolds obtained by 
gluing together two knot complements (gluing meridian to longitude). If 
the knots are non-trivial knots in S^3, we show that the Heegaard Floer 
homology of the resulting manifold has rank greater than one. By extending 
this approach to knots in arbitrary three manifolds, we hope to obtain a 
new proof of Eftekhary's claimed result that a manifold whose Heegaard 
Floer homology has rank one cannot contain an essential torus. This is 
joint work in progress with Matt Hedden.