Framed instanton homology of surgeries on L-space knots

Tye Lidman; Juanita Pinzon-Caicedo; Christopher Scaduto

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arXiv · 2003.03329

Framed instanton homology of surgeries on L-space knots

Tye Lidman·Juanita Pinzon-Caicedo·Christopher Scaduto

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Abstract

An important class of three-manifolds are L-spaces, which are rational homology spheres with the smallest possible Floer homology. For knots with an instanton L-space surgery, we compute the framed instanton Floer homology of all integral surgeries. As a consequence, if a knot has a Heegaard Floer and instanton Floer L-space surgery, then the theories agree for all integral surgeries. In order to prove the main result, we prove that the Baldwin-Sivek contact invariant in framed instanton Floer homology is homogeneous with respect to the absolute $\mathbb{Z}/2$-grading, but not the $\mathbb{Z}/4$-grading.

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BibTeX RIS

Tye Lidman, Juanita Pinzon-Caicedo, Christopher Scaduto. 2020-03-06. Framed instanton homology of surgeries on L-space knots. https://arxiv.org/abs/2003.03329

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