Abstract
This thesis proves a connected sum formula for Heegaard, instanton and monopole knot Floer homologies defined using direct limits. Our techniques rely on Sutured Floer theories and the contact gluing maps. Along the way, we prove several folklore results about the Honda-Kazez-Mati\'{c} gluing map in Heegaard Floer homology. As an application of our argument we deduce the oriented skein exact triangle for Heegaard, instanton and monopole knot Floer homology.
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