OscarCunningham, 1 month ago to random

Is there a construction like the spectrum of a ring, but that gives you an ∞-groupoid rather than a topological space?

#CategoryTheory #Topology #AlgebraicTopology

caten, 10 months ago to random

The new version of my paper with Semin Yoo, "Orientable triangulable manifolds are essentially quasigroups" is now available on arXiv! You can find the preprint at https://arxiv.org/abs/2110.05660 and you can find some videos of me talking about it on my YouTube channel (https://www.youtube.com/channel/UCT0qXiThOxzbCO36U-iXNTQ).

In addition to new images which illustrate our constructions we also have filled a gap in the proof of the main theorem. In order to show that all orientable triangulable manifolds could be created from an (n)-ary quasigroup by our construction, we needed to make an appropriate (n)-quasigroup for each manifold. What we actually did in the original paper was give a presentation of such an algebraic structure, which is not quite enough to prove the desired result. This new version contains an explicit description of such an (n)-quasigroup.

You can look forward to hearing more from me on connections between #quasigroups and #topology in the future!

#UniversalAlgebra #combinatorics #AlgebraicTopology