Special Issue — Dedicated to 60th Birthday of Jozef Przytycki; Guest Editors: M. K. Dabkowski, V. Harizanov, J. H. Przytycki, R. Sazdanovic and A. SikoraNo Access

Foundations of topological racks and quandles

Mohamed Elhamdadi

Department of Mathematics and Statistics, University of South Florida, Tampa, Florida 33620, USA

E-mail Address: emohamed@math.usf.edu

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and

El-Kaïoum M. Moutuou

School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK

E-mail Address: e.mohamedmoutuou@soton.ac.uk

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https://doi.org/10.1142/S0218216516400022Cited by:13 (Source: Crossref)

Abstract

We give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles. Central extensions of topological racks are then introduced providing a first step toward a general continuous cohomology theory for topological racks and quandles.

Keywords:

AMSC: 57M25, 57M27, 20E22, 22E41

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