Add to ORKGWe construct divide knots with arbitrary smooth four-genus but topological four-genus equal to one. In particular, for strongly quasipositive fibred knots, the ratio between the topological and the smooth four-genus can be arbitrarily close to zero.Comment: 8 pages, 3 figure
We show that a positive braid knot has maximal topological 4-genus exactly if it has maximal signatu...
We show that the difference between the genus and the stable topological 4-genus of alternating knot...
We introduce a 4-dimensional analogue of the rational Seifert genus of a knot $K\subset Y$, which we...
We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of...
This paper contains the results of efforts to determine values of the smooth and the topological sli...
AbstractBy using a result of Rudolph concerning the four-genera of classical knots, we give an infin...
We give examples of a linear combination of algebraic knots and their mirrors that are algebraically...
We present a lower bound on the stable $4$-genus of a knot based on Casson-Gordon $\tau$-signatures....
This paper presents evidence supporting the surprising conjecture that in thetopological category th...
In 1981, Freedman proved that knots with trivial Alexander polynomial bound a locally flat disc in t...
We show there exist infinitely many knots of every fixed genus $g\geq 2$ which do not admit surgery ...
We give an elementary, self-contained proof of the theorem, proven independently in 1958-9 by Crowel...
We prove that the topological locally flat slice genus of large torus knots takes up less than three...
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus o...
We study the minimal genus problem for some smooth four-manifolds.Comment: 18 page
We show that a positive braid knot has maximal topological 4-genus exactly if it has maximal signatu...
We show that the difference between the genus and the stable topological 4-genus of alternating knot...
We introduce a 4-dimensional analogue of the rational Seifert genus of a knot $K\subset Y$, which we...
We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of...
This paper contains the results of efforts to determine values of the smooth and the topological sli...
AbstractBy using a result of Rudolph concerning the four-genera of classical knots, we give an infin...
We give examples of a linear combination of algebraic knots and their mirrors that are algebraically...
We present a lower bound on the stable $4$-genus of a knot based on Casson-Gordon $\tau$-signatures....
This paper presents evidence supporting the surprising conjecture that in thetopological category th...
In 1981, Freedman proved that knots with trivial Alexander polynomial bound a locally flat disc in t...
We show there exist infinitely many knots of every fixed genus $g\geq 2$ which do not admit surgery ...
We give an elementary, self-contained proof of the theorem, proven independently in 1958-9 by Crowel...
We prove that the topological locally flat slice genus of large torus knots takes up less than three...
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus o...
We study the minimal genus problem for some smooth four-manifolds.Comment: 18 page
We show that a positive braid knot has maximal topological 4-genus exactly if it has maximal signatu...
We show that the difference between the genus and the stable topological 4-genus of alternating knot...
We introduce a 4-dimensional analogue of the rational Seifert genus of a knot $K\subset Y$, which we...