Recently, the Seiberg-Witten-Floer homology created by Kronheimer and Mrowka has important applications in Taubes' proofs of Weinstein conjecture and Arnold Chord Conjecture. Also, Cagatay Kutluhan, Yi-Jen Lee, and Clifford Taubes have a series of papers on the arxiv proving the equivalence of Heegard-Floer and Seiberg-Witten-Floer homologies. However, these are only defined for closed 3-manifolds.

My question is if there exists any version of HF or SWFH defined for 3-manifolds with boundary?