On the nonorientable four-ball genus of torus knots

Binns, Fraser; Kang, Singon; Simone, Jonathan J.; Truöl, Paula

doi:10.48550/arxiv.2109.09187

Cited by 4 publications

(7 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is unknown whether there are any knots K where (CFK(K), ι K,+ ) is inequivalent to (CFK(K), ι K,− ). The distinction between ι K,+ and ι K,− has previously been observed in [BKST21].…”

Section: Hendricks and Manolescu Consider The Mapsupporting

confidence: 55%

Naturality and functoriality in involutive Heegaard Floer homology

Hendricks¹,

Hom²,

Stoffregen³

et al. 2022

Preprint

View full text Add to dashboard Cite

We prove first-order naturality of involutive Heegaard Floer homology, and furthermore construct well-defined maps on involutive Heegaard Floer homology associated to cobordisms between three-manifolds. We also prove analogous naturality and functoriality results for involutive Floer theory for knots and links. The proof relies on the doubling model for the involution, as well as several variations.

show abstract

Section: Hendricks and Manolescu Consider The Mapsupporting

confidence: 55%

Naturality and functoriality in involutive Heegaard Floer homology

Hendricks¹,

Hom²,

Stoffregen³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Suppose that A(K) = 0. As observed in [BKST21], the involution ι K r on CF K U V (S 3 , K r ) = CF K U V (S 3 , K) is the homotopy inverse of ι K . By assumption, there exists an ι K -local map…”

Section: The Horizontal Almost ι K -Local Equivalence Groupmentioning

confidence: 56%

Torsion in the knot concordance group and cabling

Kang¹,

Park²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We define a nontrivial mod 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated (odd, 1)-cables have infinite order in the concordance group and, among them, infinitely many are linearly independent. Furthermore, by taking (2, 1)-cables of the aforementioned knots, we present an infinite family of knots which are strongly rationally slice but not slice. 2020 Mathematics Subject Classification. 57K10, 57K18. Key words and phrases. Concordance knots, cabling, Horizontal almost ι K -complex. 1 One way to prove this is to use the cabling formulae for the Ozsváth-Szabó concordance invariant τ [OS03] and the Ozsváth-Stipsicz-Szabó concordance invariant Υ [OSS17]; see e.g. [Hom14a, Theorem 1] for τ and [FPR19, Proposition 5.3] for Υ.

show abstract

“…Recently, using several types of Floer theories, the nonorientable 4-genus has been studied, for example, see [1,5,6,31,48]. For a given knot 𝐾 in 𝑆 3 , we focus on topological types of smoothly and properly embedded possibly nonorientable surfaces in 𝐷 4 bounded by 𝐾.…”

Section: Applications To Nonorientable Surfaces In 𝑫 𝟒 Bounded By Tor...mentioning

confidence: 99%

Involutions, links, and Floer cohomologies

Konno,

Miyazawa,

Taniguchi

2024

Journal of Topology

View full text Add to dashboard Cite

We develop a version of Seiberg–Witten Floer cohomology/homotopy type for a 4‐manifold with boundary and with an involution that reverses the structure, as well as a version of Floer cohomology/homotopy type for oriented links with nonzero determinant. This framework generalizes the previous work of the authors regarding Floer homotopy type for spin 3‐manifolds with involutions and for knots. Based on this Floer cohomological setting, we prove Frøyshov‐type inequalities that relate topological quantities of 4‐manifolds with certain equivariant homology cobordism invariants. The inequalities and homology cobordism invariants have applications to the topology of unoriented surfaces, the Nielsen realization problem for nonspin 4‐manifolds, and nonsmoothable unoriented surfaces in 4‐manifolds.

show abstract

On the nonorientable four-ball genus of torus knots

Cited by 4 publications

References 27 publications

Naturality and functoriality in involutive Heegaard Floer homology

Naturality and functoriality in involutive Heegaard Floer homology

Torsion in the knot concordance group and cabling

Involutions, links, and Floer cohomologies

Contact Info

Product

Resources

About