Add to ORKGWe give an elementary, self-contained proof of the theorem, proven independently in 1958-9 by Crowell and Murasugi, that the genus of an alternating knot equals half the breadth of its Alexander polynomial, and that applying Seifert's algorithm to any alternating knot diagram gives a surface of minimal genus.Comment: 6 pages, 1 figure, comments welcome
A knot made out of a string are often deformed in space without cutting open the closed knot.The def...
We introduce the notion of alteration of a surface embedded in a 3-manifold extending that of compre...
We prove the cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial....
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus o...
Let K be a knot in S3 of genus g and let n> 0: We show that if rk1HFK.K;g / < 2nC1 (where1HFK ...
This paper contains the results of efforts to determine values of the smooth and the topological sli...
We prove that the meridional rank and the bridge number of the Whitehead double of a prime algebraic...
Homogeneous links were introduced by Peter Cromwell, who pr oved that the projection surface of thes...
We introduce a new link invariant called the algebraic genus, which gives an upper bound for the top...
We prove that the partial-dual genus polynomial considered as a function on chord diagrams satisfies...
We prove that the partial-dual genus polynomial considered as a function on chord diagrams satisfies...
We introduce a numerical invariant \beta(K) of a knot K which measures how non-alternating K is. We ...
In 1898, Tait asserted several properties of alternating knot diagrams. These assertions came to be ...
By twisted quantum invariants we mean polynomial invariants of knots in the three-sphere endowed wit...
We prove that a closed embedded minimal surface in the round three-sphere which satisfies the symmet...
A knot made out of a string are often deformed in space without cutting open the closed knot.The def...
We introduce the notion of alteration of a surface embedded in a 3-manifold extending that of compre...
We prove the cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial....
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus o...
Let K be a knot in S3 of genus g and let n> 0: We show that if rk1HFK.K;g / < 2nC1 (where1HFK ...
This paper contains the results of efforts to determine values of the smooth and the topological sli...
We prove that the meridional rank and the bridge number of the Whitehead double of a prime algebraic...
Homogeneous links were introduced by Peter Cromwell, who pr oved that the projection surface of thes...
We introduce a new link invariant called the algebraic genus, which gives an upper bound for the top...
We prove that the partial-dual genus polynomial considered as a function on chord diagrams satisfies...
We prove that the partial-dual genus polynomial considered as a function on chord diagrams satisfies...
We introduce a numerical invariant \beta(K) of a knot K which measures how non-alternating K is. We ...
In 1898, Tait asserted several properties of alternating knot diagrams. These assertions came to be ...
By twisted quantum invariants we mean polynomial invariants of knots in the three-sphere endowed wit...
We prove that a closed embedded minimal surface in the round three-sphere which satisfies the symmet...
A knot made out of a string are often deformed in space without cutting open the closed knot.The def...
We introduce the notion of alteration of a surface embedded in a 3-manifold extending that of compre...
We prove the cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial....