5 citations · 7 across the 11 of their papers we have counts for
11 papers
The Conway knot has infinite concordance order
Chiara Donatone, Marc Kegel, Lukas Lewark +1
We examine how the Rasmussen invariant, satellite operations, and null-homologous twists can be used to establish infinite order of knots in the smooth concordance group. As an app…
On T-positive links
Benjamin Bode, Paula Truöl
T-positive links form a subset of strongly quasipositive links that strictly contains the set of all non-split braid positive links. Analogous to Baader's characterisation of posit…
Braid positive surgery diagrams
Marc Kegel, Paula Truöl
In this short note, we prove that every closed, oriented, connected 3-manifold arises as Dehn surgery along a braid positive link.
On the detection of knots by their traces in high dimensions
Valentina Bais, Alessio Di Prisa, Daniel Hartman +8
For every , we demonstrate the existence of non-isotopic, smooth -knots in with diffeomorphic traces. We give two proofs: the first by generalising the RBG l…
Non-complex cobordisms between quasipositive knots
Maciej Borodzik, Paula Truöl
We show that for every genus , there exist quasipositive knots and such that there is a cobordism of genus between and…
Algorithms in 4-manifold topology
Stefan Bastl, Rhuaidi Burke, Rima Chatterjee +28
We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In p…
Minimal cobordisms between thin and thick torus knots
Sebastian Baader, Lukas Lewark, Filip Misev +1
We determine the locally flat cobordism distance between torus knots with small and large braid index, up to high precision. Here small means 2, 3, 4, or 6. As an application, we d…
3-braid knots with maximal 4-genus
Sebastian Baader, Lukas Lewark, Filip Misev +1
We classify 3-braid knots whose topological 4-genus coincides with their Seifert genus, using McCoy's twisting method and the Xu normal form. In addition, we give upper bounds for…
Strongly quasipositive links are concordant to infinitely many strongly quasipositive links
Paula Truöl
We show that every non-trivial strongly quasipositive link is smoothly concordant to infinitely many pairwise non-isotopic strongly quasipositive links. In contrast to our result,…
On the nonorientable four-ball genus of torus knots
Fraser Binns, Sungkyung Kang, Jonathan Simone +1
The nonorientable four-ball genus of a knot in is the minimal first Betti number of nonorientable surfaces in bounded by . By amalgamating ideas from involutive…
The upsilon invariant at 1 of 3-braid knots
Paula Truöl
We provide explicit formulas for the integer-valued smooth concordance invariant for every 3-braid knot . We determine this invariant, which was defined b…