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• W3093454504 abstract "This paper establishes a new technique that enables us to access some fundamental structural properties of instanton Floer homology. As an application, we establish, for the first time, a relation between the instanton Floer homology of a $3$-manifold or a null-homologous knot inside a $3$-manifold and the Heegaard diagram of that $3$-manifold or knot. We further use this relation to compute the instanton knot homology of some families of $(1,1)$-knots, including all torus knots in $S^3$, which were mostly unknown before. As a second application, we also study the relation between the instanton knot homology $KHI(Y,K)$ and the framed instanton Floer homology $I^sharp(Y)$. In particular, we prove the inequality $dim_mathbb{C} I^sharp(Y)le dim_mathbb{C}KHI(Y,K)$ for all rationally null-homologous knots $Ksubset Y$ and we constructed a new decomposition of the framed instanton Floer homology of Dehn surgeries along $K$ that corresponds to the decomposition along torsion spin$^c$ decompositions in monopole and Heegaard Floer theory." @default.
• W3093454504 created "2020-10-22" @default.
• W3093454504 creator A5005698720 @default.
• W3093454504 creator A5054715840 @default.
• W3093454504 date "2022-03-01" @default.
• W3093454504 modified "2023-10-16" @default.
• W3093454504 title "Instanton Floer homology, sutures, and Heegaard diagrams" @default.
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• W3093454504 doi "https://doi.org/10.1112/topo.12218" @default.
• W3093454504 hasPublicationYear "2022" @default.
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