arXiv research

Study exact surgery formula in involutive Heegaard Floer homology.

New Heegaard Floer homology findings block chirally cosmetic surgeries.

Study cosmetic surgeries on knots in homology spheres using Casson-Walker invariant.

Surgery obstructions extended to integer homology spheres using Heegaard Floer homology.

Study calculates instanton Floer homology for surgeries on L-space knots.

The cosmetic surgery conjecture is a longstanding conjecture in 3-manifold theory. We present a theorem about exceptional cosmetic surgery for homology spheres. Along the way we prove that if the surgery is not a small seifert $\mathbb{Z}/2\mathbb{Z}$-homology sphere or a toroidal irreducible non-Seifert surgery then t…

New method proves cosmetic surgery conjecture for certain knots.

Surgery on knots can produce non-separating spheres, using Heegaard Floer homology.

New insights into cosmetic surgeries using Heegaard Floer homology.

The study determines lens spaces that can be obtained from surgeries on knots in the Poincaré homology sphere.

This paper uses Steenrod homology to simplify surgery on generalized manifolds.

Classifies surgeries on torus knots and cables that bound rational homology balls.

Proves exact triangle linking knot instanton Floer homology to surgeries.

We examine surgery on a knot in $S^3$ to determine surgery obstructions to Seifert fibered integral homology spheres. We find such surgery obstructions using Heegaard Floer, Knot Floer homology and the mapping cone formula for computing Heegaard Floer homology of surgery on a knot. Here however, we take a different app…

The paper examines conditions for contact surgeries on rational homology 3-spheres.

Study of knot Floer homology and its relation to Heegaard Floer homology via equivariant surgery.

We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsváth and Szabó's correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then turn our attention to the case of integral surgeries, with particular emphasis on p…

Enhances knot surgery formulae for instanton Floer homology.

We establish surgery formulas for filtration of the Heegaard Floer homology associated with p/q surgery on a null-homologous knot K in a three-manifold Y, induced by K_{p/q}. Here K_{p/q} is the core of the attached solid torus (which produces the surgery). This would generalize a result of Ozsvath and Szabo. We will r…

This paper explores how many positive integer surgeries on a knot produce a manifold rational homology cobordant to a lens space.

Using Taubes' periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We give an obstruction to a homology sphere being surgery on a knot coming from Heegaard Floer homology. This is used to construct infinitely man…

Let $K$ be a rationally null-homologous knot in a three-manifold $Y$. We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold obtained as Morse surgery on the knot $K$. As an application, we express the Heegaard Floer homology of rational surgerie…

It is known by the author that there exist 20 families of Dehn surgeries in the Poincaré homology sphere yielding lens spaces. In this paper, we give the concrete knot diagrams of the families and extend them to families of lens space surgeries in Brieskorn homology spheres. We illustrate families of lens space surgeri…

Study pochette surgery on 4-manifolds, focusing on 4-spheres.

The study limits the number of cosmetic surgeries for certain knots in specific 3-manifolds.

Proves a formula for instanton Floer homology of knots.

Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3-manifolds, obtained by three different Dehn surgeries on a fixed knot. In this paper, the behavior of $SU(N)$-ins…

Proves an equivariant version of Heegaard Floer link surgery formula.

A new surgery formula for knot lattice homology.

Khovanov homology remains unchanged by certain surface surgeries.

For a 3-manifold with torus boundary admitting an appropriate involution, we show that Khovanov homology provides obstructions to certain exceptional Dehn fillings. For example, given a strongly invertible knot in S^3, we give obstructions to lens space surgeries, as well as obstructions to surgeries with finite fundam…

We refine Matveev's result asserting that any two closed oriented 3-manifolds can be related by a sequence of borromean surgeries if and only if they have isomorphic first homology groups and linking pairings. Indeed, a borromean surgery induces a canonical isomorphism between the first homology groups of the involved …

We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via a topological homology cobordism preserving the homotopy classes of the meridia…

Extends Seifert algorithm to 3-manifolds via surgery.

Characterizes $(1,1)$ knots with large Dehn surgeries.

Study shows surgeries on certain knots bound rational homology 4-balls.

Using the combinatorial approach to Heegaard Floer homology we obtain a relatively easy formula for computation of hat Heegaard Floer homology for the three-manifold obtained by rational surgery on a knot K inside a homology sphere Y.

Proves SU(2) representations for certain 3-spheres with embedded tori.

We prove the existence of an exact triangle for the Pin(2)-monopole Floer homology groups of three manifolds related by specific Dehn surgeries on a given knot. Unlike the counterpart in usual monopole Floer homology, only two of the three maps are those induced by the corresponding elementary cobordism. We use this tr…

In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1. This implies that any knot with an L-space surgery has at most one reducible surgery, a fac…

Study extends contact cosmetic surgeries to non-trivial Legendrian knots in L-spaces.

By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the knot Floer homology of its (rationally null-homologous) binding. We then use this …

New homology spheres found with special knots.

Study shows constraints on cosmetic surgeries in $S^3$ for knots with specific properties.

New surgery obstructions found in simple character varieties.

Study knot invariants and surgeries, proving properties of instanton homologies.

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a non-trivial knot in the three-sphere. To obtain this result, we use a surgery long exact sequence for monopole Floer homology, together with a non-vanishing theorem, which shows that monopole Floer homolo…

For any three-manifold presented as surgery on a framed link (L,Λ) in an integral homology sphere, Manolescu and Ozsváth construct a hypercube of chain complexes whose homology calculates the Heegaard Floer homology of Λ-framed surgery on Y. This carries a natural filtration that exists on any hypercube of chain comple…