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Nontrivial Topological Quandles

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Abstract

We show that there are infinitely many nonisomorphic quandle structures on any topogical space X of positive dimension. In particular, we disprove Conjecture 5.2 in Cheng et al. (Topology Appl 248:64–74, 2018), asserting that there are no nontrivial quandle structures on the closed unit interval [0, 1].

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Acknowledgements

I would like to thank Mohamed Elhamdadi for introducing me to the subject, bringing my attention to Conjecture 5.2 in [6] and warm hospitality during my stay at the University of South Florida. I thank Mohamed Elbehiry for stimulating discussions and helpful suggestions on the improvement of the exposition. I am grateful to the reviewer for useful comments and corrections.

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  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, 15260, USA

    Boris Tsvelikhovskiy

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  1. Boris Tsvelikhovskiy
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Correspondence to Boris Tsvelikhovskiy.

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Tsvelikhovskiy, B. Nontrivial Topological Quandles. Arnold Math J. 8, 535–542 (2022). https://doi.org/10.1007/s40598-022-00212-3

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