9 papers
Genus-zero links with prescribed knots as components
Raphael Appenzeller, José Pedro Quintanilha
We prove that any finite collection of at least three isotopy classes of knots in a 3-manifold is realizable as the components of a genus-zero link in , provided that an obv…
Cobordism-equivalence for codimension-one submanifolds
Stefan Friedl, Tobias Hirsch, Clayton McDonald +2
We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositio…
All knots are trivial: a "proof" by sleight of hand
Raphael Appenzeller, José Pedro Quintanilha
We take a close look at a classical magic trick performed with a string, where a trivial knot is seemingly isotoped into a trefoil, and generalize it to a family of magic tricks fo…
Geometric invariants of TDLC completions
Ilaria Castellano, José Pedro Quintanilha
Recently, Bonn and Sauer showed that, from the point of view of compactness properties, the Schlichting completion of a Hecke pair behaves precisely as if it were the quoti…
Geometric invariants of locally compact groups: the homological perspective
Kai-Uwe Bux, Elisa Hartmann, José Pedro Quintanilha
In this paper we develop the homological version of -theory for locally compact Hausdorff groups, leaving the homotopical version for another paper. Both versions are connected…
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…