arXiv research

The paper proves finiteness of cosmetic fillings on a specific type of 3-manifold.

Update: The Cosmetic Surgery Conjecture modulo finitely many Dehn-filling coefficients has been a well-known classical result, so the first main result of this paper is not new. (But the author was initially unaware of this fact, and the tools and techniques used here are very different from all the classically known m…

The paper verifies no cosmetic surgeries on knots and 3-manifolds using hyperbolic geometry.

This paper proves explicit bilipschitz bounds on the change in metric between the thick part of a cusped hyperbolic 3-manifold N and the thick part of any of its long Dehn fillings. Given a bilipschitz constant J > 1 and a thickness constant epsilon > 0, we quantify how long a Dehn filling suffices to guarantee a J-bil…

We prove that for any V>0, there exist a hyperbolic manifold M_V, so that Vol(M_V) < 2.03 and LinVol(M_V) > V. The proof requires study of cosmetic surgery on links (equivalently, fillings of manifolds with boundary tori). There is no bound on the number of components of the link (or boundary components). For statement…

This paper concerns the Dehn surgery construction, especially those Dehn surgeries leaving the manifold unchanged. In particular, we describe an oriented 1-cusped hyperbolic 3-manifold X with a pair of slopes r_1, r_2 such that the Dehn filled manifolds X(r_1), X(r_2) are oppositely oriented copies of the lens space L(…

Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots $K$ and $K'$ of the same square-free determinant are related by a band surgery, then the absolute value of the difference in their signatures is either 0 or 8. This obstruction follows from a …

Study finds chirally cosmetic surgeries on knots and manifolds, contradicting previous conjectures.

Two knot families meet cosmetic surgery conjecture.

Paper restricts chirally cosmetic surgeries on knots.

Study confirms contact cosmetic surgery for most knots, with exceptions.

New findings on cosmetic surgeries for satellite knots.

This paper concerns the truly or purely cosmetic surgery conjecture. We give a survey on exceptional surgeries and cosmetic surgeries. We prove that the slope of an exceptional truly cosmetic surgery on a hyperbolic knot in $S^3$ must be $\pm 1$ and the surgery must be toroidal but not Seifert fibred. As consequence we…

Cosmetic surgeries on pretzel knots are unique.

3-braid knots can't have purely cosmetic surgeries.

Study shows most odd pretzel knots don't allow chirally cosmetic surgeries.

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…

Study proves nontrivial knots can't undergo cosmetic surgeries.

Proves cosmetic crossing conjecture for certain knots.

The study shows a limit on cosmetic surgeries for certain knots.

Study knots with genus one, finds Gordian distance and cosmetic crossing constraints.

The study proves large alternating Montesinos knots cannot have purely cosmetic surgeries.

Proves cosmetic surgery conjecture for strongly invertible knots.

New Heegaard Floer homology findings block chirally cosmetic surgeries.

Paper proves knots satisfy a conjecture using Jones polynomial.

Study shows most knots up to 10 crossings can't be chirally cosmetic.

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

Two Dehn surgeries on a knot are called cosmetic if they yield homeomorphic manifolds. For a null-homologous knot with certain conditions on the Thurston norm of the ambient manifold, if the knot admits cosmetic surgeries, then the surgery coefficients are equal up to sign.

Alexander polynomial condition blocks crossing changes in some knots.

Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in $S^3$ do not admit purely cosmetic surgeries. In this article, we confirm this conjecture for cable knots.

In this paper, we prove that there are no truly cosmetic surgeries on genus one classical knots. If the two surgery slopes have the same sign, we give the only possibilities of reflectively cosmetic surgeries. The result is an application of Heegaard Floer theory and number theory.

We prove that the property of admitting no cosmetic crossing changes is preserved under the operation of forming certain satellites of winding number zero. We also define strongly cosmetic crossing changes and we discuss their behavior under the operation of inserting full twists in the strings of closed braids.

The study confirms that most positive 2-bridge knots up to 31 crossings do not have chirally cosmetic surgeries.

New quantum obstructions prevent purely cosmetic surgeries on knots.

Proves special alternating knots can't have cosmetic crossings.

We show that a $(p,q)$-cable of a non-trivial knot $K$ does not admit chirally cosmetic surgery for $q\neq 2$, or $q=2$ with additional assumptions. In particular, we show that $(p,q)$-cable of non-trivial knot $K$ does not admit chirally cosmetic surgery as long as the JSJ piece of knot exterior does not contain $(2,r…

We present various examples of cosmetic bandings on knots and links, that is, bandings on knots and links leaving their types unchanged. As a byproduct, we give a hyperbolic knot which admits exotic chirally cosmetic surgeries yielding hyperbolic manifolds. This gives a counterexample to a conjecture raised by Bleiler,…

Formula for Casson-Walker invariant; applies to knot complements and cosmetic crossing conjecture.

Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in $S^3$ do not admit purely cosmetic surgeries. In this article, we confirm this conjecture for connected sums of knots by analysing the JSJ-structures.

Let K' be a knot that admits no cosmetic crossing changes and let C be a non-trivial, prime, non-cable knot. Then any knot that is a satellite of C with winding number zero and pattern K' admits no cosmetic crossing changes. As a consequence we prove the nugatory crossing conjecture for Whitehead doubles of prime, non-…

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

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

Study finds new knot distances and chirally cosmetic bands using grid diagrams.

New proof for a knot type not admitting certain surgeries.

We show that if K is a satellite knot which admits a generalized cosmetic crossing change of order q with |q| \geq 6, then K admits a pattern knot with a generalized cosmetic crossing change of the same order. As a consequence of this, we find that any prime satellite knot which admits a pattern knot that is fibered ca…

Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$, we show that the two surgery slopes must be the opposite of each other. One ingredient of our proof is a Dehn surgery form…

New insights into cosmetic surgeries using Heegaard Floer homology.

We consider the cosmetic surgery problem for two-bridge knots in the 3-sphere. It is seen that all the two-bridge knots at most 9 crossings other than $9_{27} = S(49,19)=C[2,2,-2,2,2,-2]$ admits no purely cosmetic surgery pairs. Then we show that any two-bridge knot of the Conway form $[2x,2,-2x,2x,2,-2x]$ with $x \ge …