3 papers
math.GT2026
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…
math.GT2026
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…
math.GT2025
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…