Marco Marengon

activity

20142026

most citedConcordance maps in knot Floer homology

16 citations · 41 across the 15 of their papers we have counts for

collaborators

18 papers

math.GT2026

A note on smoothly slice links in $S^{2} \times S^{2}$

Marco Marengon, Clayton McDonald

We give an alternative proof of a result of Miyazaki and Yasuhara that there exists links that are not smoothly slice in $S^{2} \times S^{2}$ . We discuss potential applications to the…

math.GT2024

Correction terms of double branched covers and symmetries of immersed curves

Jonathan Hanselman, Marco Marengon, Biji Wong

We use the immersed curves description of bordered Floer homology to study $d$ -invariants of double branched covers $Σ_{2} (L)$ of arborescent links $L \subset S^{3}$ . We define a new i…

math.GT2024

Splitting links by integer homology spheres

Marco Golla, Marco Marengon

For every $n \geq 3$ , we construct 2-component links in $S^{n + 1}$ that are a split by an integer homology $n$ -sphere, but not by $S^{n}$ . In the special case $n = 3$ , i.e. that of 2-lin…

math.GT2024

Smoothly slice links in $CP^{2} # CP^{2}$

Marco Marengon, Clayton McDonald

We show that there exists a link with 2 components which is not smoothly slice in $CP^{2} # CP^{2}$ . By contrast, it is well-known that every knot (i.e.,…

math.GT2024

Spectra in Khovanov and knot Floer theories

Marco Marengon, Sucharit Sarkar, Andras Stipsicz

These notes provide an introduction to the stable homotopy types in Khovanov theory (due to Lipshitz-Sarkar) and in knot Floer theory (due to Manolescu-Sarkar). They were written f…

math.GT2023

On the rank of knot homology theories and concordance

Nathan M. Dunfield, Sherry Gong, Thomas Hockenhull +2

For a ribbon knot, it is a folk conjecture that the rank of its knot Floer homology must be 1 modulo 8, and another folk conjecture says the same about reduced Khovanov homology. W…

math.GT2022★ 2 cited

A note on surfaces in $CP^{2}$ and $CP^{2} # CP^{2}$

Marco Marengon, Allison N. Miller, Arunima Ray +1

In this brief note, we investigate the $CP^{2}$ -genus of knots, i.e. the least genus of a smooth, compact, orientable surface in $CP^{2} ∖ B^{4} ˚$ boun…

math.GT2022★ 1 cited

Unknotting number 21 knots are slice in K3

Marco Marengon, Stefan Mihajlović

We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree…

math.GT2020★ 7 cited

Relative genus bounds in indefinite four-manifolds

Ciprian Manolescu, Marco Marengon, Lisa Piccirillo

Given a closed four-manifold $X$ with an indefinite intersection form, we consider smoothly embedded surfaces in $X ∖$ int $(B^{4})$ , with boundary a knot $K \subset S^{3}$ . We…

math.GT2020★ 3 cited

Non-orientable link cobordisms and torsion order in Floer homologies

Sherry Gong, Marco Marengon

We use unoriented versions of instanton and knot Floer homology to prove inequalities involving the Euler characteristic and the number of local maxima appearing in unorientable co…

math.GT2019★ 1 cited

A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds

Ciprian Manolescu, Marco Marengon, Sucharit Sarkar +1

We extend the definition of Khovanov-Lee homology to links in connected sums of $S^{1} \times S^{2}$ 's, and construct a Rasmussen-type invariant for null-homologous links in these mani…

math.GT2019★ 6 cited

Strands algebras and Ozsváth-Szabó's Kauffman-states functor

Andrew Manion, Marco Marengon, Michael Willis

We define new differential graded algebras A(n,k,S) in the framework of Lipshitz-Ozsváth-Thurston's and Zarev's strands algebras from bordered Floer homology. The algebras A(n,k,S)…

math.GT2019★ 2 cited

Generators, relations, and homology for Ozsváth-Szabó's Kauffman-states algebras

Andrew Manion, Marco Marengon, Michael Willis

We give a generators-and-relations description of differential graded algebras recently introduced by Ozsváth and Szabó for the computation of knot Floer homology. We also compute…

math.GT2018

The Knight Move Conjecture is false

Ciprian Manolescu, Marco Marengon

The Knight Move Conjecture claims that the Khovanov homology of any knot decomposes as direct sums of some "knight move" pairs and a single "pawn move" pair. This is true for insta…

math.GT2016

Correction terms and the non-orientable slice genus

Marco Golla, Marco Marengon

By considering negative surgeries on a knot $K$ in $S^{3}$ , we derive a lower bound to the non-orientable slice genus $γ_{4} (K)$ in terms of the signature $σ (K)$ and the concordance in…

math.GT2015★ 16 cited

Concordance maps in knot Floer homology

Andras Juhasz, Marco Marengon

We show that a decorated knot concordance $C$ from $K$ to $K^{'}$ induces a homomorphism $F_{C}$ on knot Floer homology that preserves the Alexander and Maslov gradings. Furthermore, it…

math.GT2015

Computing cobordism maps in link Floer homology and the reduced Khovanov TQFT

András Juhász, Marco Marengon

We study the maps induced on link Floer homology by elementary decorated link cobordisms. We compute these for births, deaths, stabilizations, and destabilizations, and show that s…

math.GT2014★ 3 cited

On $d$ -invariants and generalised Kanenobu knots

Marco Marengon

We prove that for particular infinite families of $L$ -spaces, arising as branched double covers, the $d$ -invariants defined by Ozsváth and Szabó are arbitrarily large and small. As…

A note on smoothly slice links in S2×S2

Correction terms of double branched covers and symmetries of immersed curves

Splitting links by integer homology spheres

Smoothly slice links in CP2#CP2

Spectra in Khovanov and knot Floer theories

On the rank of knot homology theories and concordance

A note on surfaces in CP2 and CP2#CP2

Unknotting number 21 knots are slice in K3

Relative genus bounds in indefinite four-manifolds

Non-orientable link cobordisms and torsion order in Floer homologies

A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds

Strands algebras and Ozsváth-Szabó's Kauffman-states functor

Generators, relations, and homology for Ozsváth-Szabó's Kauffman-states algebras

The Knight Move Conjecture is false

Correction terms and the non-orientable slice genus

Concordance maps in knot Floer homology

Computing cobordism maps in link Floer homology and the reduced Khovanov TQFT

On d-invariants and generalised Kanenobu knots

A note on smoothly slice links in $S^{2} \times S^{2}$

Smoothly slice links in $CP^{2} # CP^{2}$

A note on surfaces in $CP^{2}$ and $CP^{2} # CP^{2}$

On $d$ -invariants and generalised Kanenobu knots