Involutive Heegaard Floer homology
By Kristen Hendricks, Ciprian Manolescu. 2015
141 citations recorded by the source corpus.
Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to $\mathbb{Z}_4$-equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, $\underline{d}$ and $\bar{d}$, and two invariants of smooth knot concordance, $\underline{V}_0$ and $\overline{V}_0$. We also develop a formula for the involutive Heegaard Floer homology of large integral surgeries on knots. We give explicit calculations in the case of L-space knots and thin knots. In particular, we show that $\underline{V}_0$ detects the non-sliceness of the figure-eight knot. Other applications include constraints on which large surgeries on alternating knots can be homology cobordant to other large surgeries on alternating knots.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ac4e8e9c645174241919d64781857f128207c6bb
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
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Citations in the corpus
- Quasi-stabilization and basepoint moving maps in link Floer homology (2016, background): “ses correspond to setting various variables equal to zero in the formula for & . In addition, we consider the eect of another dieomorphism which naturally appears in the involutive setting (cf. [HM15]). Suppose that Kis a component of a link L and suppose that the basepoints of K are z 1;w 1; ;z”
- Link cobordisms and absolute gradings in link Floer homology (2017, background): “t just intersection points) by declaring it to be linear in the U tvariables for t2p[q. By the above formula of Spincstructures, we see that maps 44 IAN ZEMKE CFL(Y;L;s) to CFL(Y;L;s+PD[L]). As in [HM15], the map commutes with change of diagrams maps, up to equivariant ltered chain homotopy. In this”
- Connected sums and involutive knot Floer homology (2017, methodology): “In addition, the author owes an intellectual debt to Kristen Hendricks and Ciprian Manolescu who coauthored a similar paper with the author and provided many of the ideas and arguments in that context.”