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On Floer minimal knots in sutured manifolds

2021/08/24 by Zhenkun Li, Yi Xie, Li, Zhenkun +3 · 1 citation
Mathematics · Medicine · #Geometric and Algebraic Topology #Botulinum Toxin and Related Neurological Disorders

paper · pdf · doi:10.48550/arxiv.2108.10933

Abstract

Suppose (M, γ) is a balanced sutured manifold and K is a rationally null-homologous knot in M. It is known that the rank of the sutured Floer homology of M\backslash N(K) is at least twice the rank of the sutured Floer homology of M. This paper studies the properties of K when the equality is achieved for instanton homology. As an application, we show that if L⊂ S3 is a fixed link and K is a knot in the complement of L, then the instanton link Floer homology of L∪ K achieves the minimum rank if and only if K is the unknot in S3\backslash L.

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