geometry dash apk Arnaud de Mesmay (CNRS) - Hard embedding problems in three dimensions

Computation in geometric topology
14 December 2017

Abstract: While the search for efficient algorithms to solve three-dimensional topological problems has been very active in the past decades, results on computational hardness have been comparatively very scarce. In this talk, we will present two NP-hardness proofs for problems on embeddings into three-manifolds. The first one is about finding an embedded non-orientable surface of Euler genus g in a triangulated three-manifold, and the second one is about deciding whether a two- or three-dimensional complex embeds into R^3. This hardness stands in stark contrast with the lower dimensional cases which can be solved in linear time, and a variety of computational problems in S^3 like unknot or three-sphere recognition which are in NP and co-NP (assuming the generalized Riemann hypothesis). This is based on joint work with Benjamin Burton, Yo'av Rieck, Eric Sedgwick, Martin Tancer and Uli Wagner.

geometry dash apk Arnaud de Mesmay (CNRS) - Hard embedding problems in three dimensions
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