6 papers
Formalizing Abstract Simplicial Complexes & Stellar Subdivisions in Lean
Garett Cunningham, Daniel Zach, Stefan Friedl
The theory of simplicial complexes is a cornerstone of topology, offering a sophisticated tool for computing invariants. We present a formalization of abstract simplicial complexes…
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…
The Unsolvability of the Homeomorphism Problem
Stefan Friedl, Tobias Hirsch, Marc Kegel
In this short expository note, we give a detailed proof of Markov's theorem on the unsolvability of the homeomorphism problem and of the existence of unrecognizable manifolds in al…
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…
Bounding the ribbon numbers of knots and links
Stefan Friedl, Filip Misev, Alexander Zupan
The ribbon number of a ribbon knot is the minimal number of ribbon intersections contained in any ribbon disk bounded by . We find new lower bounds for $r…
Writhe invariants of 3-regular spatial graphs
Stefan Friedl, Tejas Kalelkar, José Pedro Quintanilha
We give a necessary condition for two diagrams of -regular spatial graphs with the same underlying abstract graph to represent isotopic spatial graphs. The test works by rea…