We develop monopole and instanton Floer homology groups for balanced sutured manifolds, in the spirit of A. Juhász. "Holomorphic discs and sutured manifolds." Algebr. Geom. Topol., 6:1429–1457 (electronic), 2006. Applications include a new proof of Property P for knots.
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Kronheimer et al. (2010) studied this question.
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