arXiv research

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

Study of cosmetic contact surgeries on knots, excluding some cases.

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

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

Two knot families meet cosmetic surgery conjecture.

Cosmetic surgeries on pretzel knots are unique.

Paper restricts chirally cosmetic surgeries on 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…

New findings on cosmetic surgeries for satellite knots.

New Heegaard Floer homology findings block chirally cosmetic surgeries.

Study chirally cosmetic surgeries on knots with constraints and invariants.

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…

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

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

The LMO invariant helps find constraints for cosmetic surgeries on knots.

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

Cable knots can't have homeomorphic surgeries.

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

Study proves nontrivial knots can't undergo cosmetic surgeries.

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

Study shows knots in Poincaré sphere can't be 'cosmetically' altered.

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.

Study shows $(p,q)$-cable knots cannot undergo certain types of surgery.

Research confirms non-trivial knots in S^3 do not admit purely cosmetic surgeries.

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.

New proof for a knot type not admitting certain surgeries.

New method proves cosmetic surgery conjecture for certain knots.

New quantum obstructions prevent purely cosmetic surgeries on knots.

Paper proves knots satisfy a conjecture using Jones polynomial.

New insights into cosmetic surgeries using Heegaard Floer homology.

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

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

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…

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

Proves cosmetic surgery conjecture for strongly invertible knots.

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

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

The paper generalizes a surgery conjecture and proves it under the Zilber-Pink conjecture.

Study sharp bounds on knot surgeries in specific manifolds.

Special knots with many twists have no certain type of surgery.

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 …

By considering non-orientable surfaces in the surgered manifolds, we show that the 10/3- and -10/3-Dehn surgeries on the 2-bridge knot $9_{27} = S(49,19)$ are not cosmetic, i.e., they give mutually non-homeomorphic manifolds. The knot is unknown to have no cosmetic surgeries by previously known results; in particular, …

We show that two Dehn surgeries on a knot $K$ never yield manifolds that are homeomorphic as oriented manifolds if $V_K''(1)\neq 0$ or $V_K'''(1)\neq 0$. As an application, we verify the cosmetic surgery conjecture for all knots with no more than $11$ crossings except for three $10$-crossing knots and five $11$-crossin…

Two-bridge knots can't be transformed into each other by certain surgeries.

The paper examines cosmetic two-strand twists on fibered knots and their properties.

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…

Band surgery affects knot signatures by 0 or 8.

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,…