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

The LOOPS'23 conference on #loops and #quasigroups just concluded. There were lots of great talks, great Polish food, and great people. This palace in Będlewo, Poland was a neat venue at which to study #AbstractAlgebra!

#conferences #UniversalAlgebra #math #combinatorics