Equivalence of Contact Gluing Maps in Sutured Floer Homology

Salmoiraghi, Federico

doi:10.31390/gradschool_dissertations.5017

DOI: 10.31390/gradschool_dissertations.5017

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Equivalence of Contact Gluing Maps in Sutured Floer Homology

Federico Salmoiraghi¹

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An Enhanced Euler Characteristic of Sutured Instanton Homology

2023

International Mathematics Research Notices

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For a balanced sutured manifold $(M,\gamma )$, we construct a decomposition of $SHI(M,\gamma )$ with respect to torsions in $H=H_{1}(M;\mathbb {Z})$, which generalizes the decomposition of $I^{\sharp }(Y)$ in a previous work of the authors. This decomposition can be regarded as a candidate for the counterpart of the torsion spin$^{c}$ decompositions in $SFH(M,\gamma )$. Based on this decomposition, we define an enhanced Euler characteristic $\chi _{\textrm {en}}(SHI(M,\gamma ))\in \mathbb {Z}[H]/\pm H$ and prove that $\chi _{\textrm {en}}(SHI(M,\gamma ))=\chi (SFH(M,\gamma ))$. This provides a better lower bound on $\dim _{\mathbb {C}}SHI(M,\gamma )$ than the graded Euler characteristic $\chi _{\textrm {gr}}(SHI(M,\gamma ))$. As applications, we prove instanton knot homology detects the unknot in any instanton L-space and show that the conjecture $KHI(Y,K)\cong \widehat {HFK}(Y,K)$ holds for all $(1,1)$-L-space knots and constrained knots in lens spaces, which include all torus knots and many hyperbolic knots in lens spaces.

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An Enhanced Euler Characteristic of Sutured Instanton Homology

2023

International Mathematics Research Notices

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Equivalence of Contact Gluing Maps in Sutured Floer Homology

Cited by 1 publication

References 8 publications

An Enhanced Euler Characteristic of Sutured Instanton Homology

An Enhanced Euler Characteristic of Sutured Instanton Homology

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