arXiv research

Paper restricts chirally cosmetic surgeries on knots.

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

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

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

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…

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

New Heegaard Floer homology findings block chirally cosmetic surgeries.

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

Study proves nontrivial knots can't undergo cosmetic surgeries.

We study chirally cosmetic surgeries, that is, a pair of Dehn surgeries on a knot producing homeomorphic 3-manifolds with opposite orientations. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredients are the original and the $SL(2,\mathbb{C})$ version of Casson invariant…

New proof for a knot type not admitting certain surgeries.

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

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,…

We study small Seifert possibly chiral cosmetic surgeries on not necessarily null-homologous knot in rational homology spheres. Using $PSL_2(\mathbb{C})$-character variety theory we give a sharp bound on the number of slopes producing the same small Seifert manifold if the ambient manifold satisfies some representation…

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

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 surgeries between lens spaces using Heegaard Floer d-invariant.

The paper explores surgeries on lens spaces and their knot properties.

Two knot families meet cosmetic surgery conjecture.

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.

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

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…

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.

Paper proves knots satisfy a conjecture using Jones polynomial.

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.

New quantum obstructions prevent purely cosmetic surgeries on knots.

Proves special alternating knots can't have cosmetic crossings.

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.

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.