wovepaper — the arXiv observatory

papers

Publications (31)

math.GT2026

Triangulating Spun 2-Knot Complements

Rhuaidi Antonio Burke, Benjamin Burton, Arunima Ray +3

A $2$ -knot is an embedding of a $2$ -sphere into the $4$ -sphere. Similar to the case of embedding circles into the $3$ -sphere, this allows the $2$ -sphere to be knotted. In this shor…

math.GT2019

Null, recursively starlike-equivalent decompositions shrink

Jeffrey Meier, Patrick Orson, Arunima Ray

A subset $E$ of a metric space $X$ is said to be starlike-equivalent if it has a neighbourhood which is mapped homeomorphically into $R^{n}$ for some $n$ , sending $E$ to a s…

math.GT2018

Concordance of knots in $S^{1} \times S^{2}$

Christopher W. Davis, Matthias Nagel, JungHwan Park +1

We establish a number of results about smooth and topological concordance of knots in $S^{1} \times S^{2}$ . The winding number of a knot in $S^{1} \times S^{2}$ is defined to be its class in…

math.GT2024

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.GT2014

Satellite operators with distinct iterates in smooth concordance

Arunima Ray

Let P be a knot in an unknotted solid torus (i.e. a satellite operator or pattern), K a knot in S^3 and P(K) the satellite of K with pattern P. For any satellite operator P, this c…

math.GT2025

The 4-dimensional disc embedding theorem and dual spheres

Mark Powell, Arunima Ray, Peter Teichner

We modify the proof of the disc embedding theorem for $4$ -manifolds, which appeared as Theorem 5.1A in the book "Topology of 4-manifolds" by Freedman and Quinn, in order to constru…

math.GT2023

Embedding surfaces in 4-manifolds

Daniel Kasprowski, Mark Powell, Arunima Ray +1

We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is…

math.GT2015

Shake slice and shake concordant knots

Tim D. Cochran, Arunima Ray

A crucial step in the surgery-theoretic program to classify smooth manifolds is that of representing a middle--dimensional homology class by a smoothly embedded sphere. This step f…

math.GT2023

Counterexamples in 4-manifold topology

Daniel Kasprowski, Mark Powell, Arunima Ray

We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds a…

math.GT2021

Slicing knots in definite 4-manifolds

Alexandra Kjuchukova, Allison N. Miller, Arunima Ray +1

We study the $CP^{2}$ -slicing number of knots, i.e. the smallest $m \geq 0$ such that a knot $K \subseteq S^{3}$ bounds a properly embedded, null-homologous disk in a punctured…

math.GT2025

Homotopy classification of $4$ -manifolds with $3$ -manifold fundamental group

Jonathan Hillman, Daniel Kasprowski, Mark Powell +1

We give a criterion on a group $I ¨ $ and a homomorphism $w : I ¨ \to C_{2}$ under which closed $4$ -manifolds with fundamental group $I ¨ $ and orientation character $w$ are classifie…

math.GT2016

A new family of links topologically, but not smoothly, concordant to the Hopf link

Christopher W. Davis, Arunima Ray

We give new examples of 2-component links with linking number one and unknotted components that are topologically concordant to the positive Hopf link, but not smoothly so - in fac…

math.GT2018

On the Upsilon invariant and satellite knots

Peter Feller, JungHwan Park, Arunima Ray

We study the effect of satellite operations on the Upsilon invariant of Ozsvath-Stipsicz-Szabo. We obtain results concerning when a knot and its satellites are independent; for exa…

math.GT2025

Constructing locally flat surfaces in 4-manifolds

Arunima Ray

There are two main approaches to building locally flat embedded surfaces in 4-manifolds: direct methods which geometrically manipulate a given map of a surface, and more indirect m…

math.GT2023

Gluck twists on concordant or homotopic spheres

Daniel Kasprowski, Mark Powell, Arunima Ray

Let $M$ be a compact $4$ -manifold and let $S$ and $T$ be embedded $2$ -spheres in $M$ , both with trivial normal bundle. We write $M_{S}$ and $M_{T}$ for the $4$ -manifolds obtained by th…

math.GT2021

Average four-genus of two-bridge knots

Sebastian Baader, Alexandra Kjuchukova, Lukas Lewark +2

We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.

math.GT2014

Casson towers and filtrations of the smooth knot concordance group

Arunima Ray

The n-solvable filtration ${F_{n}}_{n = 0}^{\infty}$ of the smooth knot concordance group (denoted by $C$ ), due to Cochran-Orr-Teichner, has been instrumental in th…

math.GT2020

Embedding spheres in knot traces

Peter Feller, Allison N. Miller, Matthias Nagel +3

The trace of $n$ -framed surgery on a knot in $S^{3}$ is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a mani…

math.GT2020

On distinct finite covers of 3-manifolds

Stefan Friedl, JungHwan Park, Bram Petri +2

Every closed orientable surface S has the following property: any two connected covers of S of the same degree are homeomorphic (as spaces). In this, paper we give a complete class…

math.GT2013

Injectivity of satellite operators in knot concordance

Tim D. Cochran, Christopher W. Davis, Arunima Ray

Let P be a knot in a solid torus, K a knot in 3-space and P(K) the satellite knot of K with pattern P. This defines an operator on the set of knot types and induces a satellite ope…

math.GT2026

On a volume invariant of 3-manifolds

Marc Kegel, Arunima Ray, Jonathan Spreer +2

This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complemen…

math.GT2023

Slice knots and knot concordance

Arunima Ray

These notes were prepared to accompany a sequence of three lectures at the conference Winterbraids XI in Dijon, held in December 2021. In them, we provide an introduction to slice…

math.GT2017

A family of non-split topologically slice links with arbitrarily large smooth slice genus

JungHwan Park, Arunima Ray

We construct an infinite family of topologically slice 2--component boundary links $ℓ_{i}$ , none of which is smoothly concordant to a split link, such that $g_{4} (ℓ_{i}) = i$ .

math.GT2025

Not all knots are smoothly round handle slice

Tye Lidman, Allison N. Miller, Arunima Ray

Freedman and Krushkal showed that if the surgery conjecture and the $s$ -cobordism conjecture hold for all topological 4-manifolds, then every link with pairwise zero linking number…

math.GT2026

Isotopy and equivalence of knots in 3-manifolds

Paolo Aceto, Corey Bregman, Christopher W. Davis +2

We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irred…

math.GT2025

On the detection of knotted spheres by their traces in high dimensions

Valentina Bais, Alessio Di Prisa, Daniel Hartman +8

For every $n \geq 4$ , we demonstrate the existence of non-isotopic smooth $(n - 2)$ -knots in $S^{n}$ with diffeomorphic traces by generalising the RBG link construction to all dimensio…

math.GT2018

Linear independence of cables in the knot concordance group

Christopher W. Davis, JungHwan Park, Arunima Ray

We produce infinite families of knots ${K^{i}}_{i \geq 1}$ for which the set of cables ${K_{p, 1}^{i}}_{i, p \geq 1}$ is linearly independent in the knot concordance group. We arrange…

math.GT2017

4-dimensional analogues of Dehn's lemma

Arunima Ray, Daniel Ruberman

We investigate certain $4$ -dimensional analogues of the classical $3$ -dimensional Dehn's lemma, giving examples where such analogues do or do not hold, in the smooth and topologica…

math.GT2020

Pretzel links, mutation, and the slice-ribbon conjecture

Paolo Aceto, Min Hoon Kim, JungHwan Park +1

Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P(p,q,-p,-q) is not slice, even though it has a ribbon mutant, by using 3-fold branched…

math.GT2015

Satellite operators as group actions on knot concordance

Christopher W. Davis, Arunima Ray

Any knot in a solid torus, called a pattern or satellite operator, acts on knots in the 3-sphere via the satellite construction. We introduce a generalization of satellite operator…

math.GT2013

Slice knots which bound punctured Klein bottles

Arunima Ray

We investigate the properties of knots in S^3 which bound Klein bottles, such that a pushoff of the knot has zero linking number with the knot, i.e. has zero framing. This is motiv…

Publications (31)

Triangulating Spun 2-Knot Complements

Null, recursively starlike-equivalent decompositions shrink

Concordance of knots in S1×S2

A note on surfaces in CP2 and CP2#CP2

Satellite operators with distinct iterates in smooth concordance

The 4-dimensional disc embedding theorem and dual spheres

Embedding surfaces in 4-manifolds

Shake slice and shake concordant knots

Counterexamples in 4-manifold topology

Slicing knots in definite 4-manifolds

Homotopy classification of 4-manifolds with 3-manifold fundamental group

A new family of links topologically, but not smoothly, concordant to the Hopf link

On the Upsilon invariant and satellite knots

Constructing locally flat surfaces in 4-manifolds

Gluck twists on concordant or homotopic spheres

Average four-genus of two-bridge knots

Casson towers and filtrations of the smooth knot concordance group

Embedding spheres in knot traces

On distinct finite covers of 3-manifolds

Injectivity of satellite operators in knot concordance

On a volume invariant of 3-manifolds

Slice knots and knot concordance

A family of non-split topologically slice links with arbitrarily large smooth slice genus

Not all knots are smoothly round handle slice

Isotopy and equivalence of knots in 3-manifolds

On the detection of knotted spheres by their traces in high dimensions

Linear independence of cables in the knot concordance group

4-dimensional analogues of Dehn's lemma

Pretzel links, mutation, and the slice-ribbon conjecture

Satellite operators as group actions on knot concordance

Slice knots which bound punctured Klein bottles

Concordance of knots in $S^{1} \times S^{2}$

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

Homotopy classification of $4$ -manifolds with $3$ -manifold fundamental group