Abstract: Series on Knots and EverythingIntroductory Lectures on Knot Theory, pp. 22-53 (2011) No AccessA SURVEY OF QUANDLE IDEASJ. Scott CarterJ. Scott CarterUniversity of South Alabama, USASupported in part by NSF Grant DMS #0603926.https://doi.org/10.1142/9789814313001_0002Cited by:24 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: This article surveys many aspects of the theory of quandles which algebraically encode the Reidemeister moves. In addition to knot theory, quandles have found applications in other areas which are only mentioned in passing here. The main purpose is to give a short introduction to the subject and a guide to the applications that have been found thus far for quandle cocycle invariants. FiguresReferencesRelatedDetailsCited By 24On core quandles of groupsGeorge M. Bergman15 February 2021 | Communications in Algebra, Vol. 49, No. 6The Chord Index, its Definitions, Applications, and GeneralizationsZhiyun Cheng30 January 2020 | Canadian Journal of Mathematics, Vol. 73, No. 3Symplectic quandles and parabolic representations of 2-bridge knots and linksKyeonghee Jo and Hyuk Kim20 August 2020 | International Journal of Mathematics, Vol. 31, No. 10Embeddings of quandles into groupsValeriy Bardakov and Timur Nasybullov31 July 2019 | Journal of Algebra and Its Applications, Vol. 19, No. 07Link quandles are residually finiteValeriy G. Bardakov, Mahender Singh and Manpreet Singh14 October 2019 | Monatshefte für Mathematik, Vol. 191, No. 4From biquandle structures to Hom-biquandlesE. Horvat and A. S. Crans18 March 2020 | Journal of Knot Theory and Its Ramifications, Vol. 29, No. 02Free quandles and knot quandles are residually finiteValeriy Bardakov, Mahender Singh and Manpreet Singh8 April 2019 | Proceedings of the American Mathematical Society, Vol. 147, No. 8Automorphism groups of quandles and related groupsV. Bardakov, T. Nasybullov and M. Singh8 June 2018 | Monatshefte für Mathematik, Vol. 189, No. 1The braid shelfPatrick Dehornoy25 October 2018 | Journal of Knot Theory and Its Ramifications, Vol. 27, No. 11Applications of self-distributivity to Yang–Baxter operators and their cohomologyVictoria Lebed25 October 2018 | Journal of Knot Theory and Its Ramifications, Vol. 27, No. 11Automorphism groups of quandles arising from groupsValeriy G. Bardakov, Pinka Dey and Mahender Singh15 October 2016 | Monatshefte für Mathematik, Vol. 184, No. 4Free medial quandlesPřemysl Jedlička, Agata Pilitowska and Anna Zamojska-Dzienio23 May 2017 | Algebra universalis, Vol. 78, No. 1The degenerate distributive complex is degenerateJózef H. Przytycki and Krzysztof K. Putyra20 October 2016 | European Journal of Mathematics, Vol. 2, No. 4Classification of flat connected quandlesMahender Singh29 November 2016 | Journal of Knot Theory and Its Ramifications, Vol. 25, No. 13On Classification of Quandles of Cyclic TypeSeiichi KAMADA, Hiroshi TAMARU and Koshiro WADA1 Jun 2016 | Tokyo Journal of Mathematics, Vol. 39, No. 1Laver's results and low-dimensional topologyPatrick Dehornoy19 December 2015 | Archive for Mathematical Logic, Vol. 55, No. 1-2A structural aspect of the category of quandlesDominique Bourn (France)23 October 2015 | Journal of Knot Theory and Its Ramifications, Vol. 24, No. 12Positive quandle homology and its applications in knot theoryZhiyun Cheng and Hongzhu Gao22 April 2015 | Algebraic & Geometric Topology, Vol. 15, No. 2On factorization systems for surjective quandle homomorphismsValérian Even (Belgium) and Marino Gran (Belgium)21 December 2014 | Journal of Knot Theory and Its Ramifications, Vol. 23, No. 11Quandle colorings of knots and applicationsW. Edwin Clark (USA), Mohamed Elhamdadi (USA), Masahico Saito (USA), and Timothy Yeatman (USA)1 September 2014 | Journal of Knot Theory and Its Ramifications, Vol. 23, No. 06Two- and three-cocycles for Laver tablesPatrick Dehornoy (France & France) and Victoria Lebed (Japan)17 June 2014 | Journal of Knot Theory and Its Ramifications, Vol. 23, No. 04Distributivity in Quandles and QuasigroupsMohamed Elhamdadi18 June 2014Two-point homogeneous quandles with prime cardinalityHiroshi TAMARU1 Oct 2013 | Journal of the Mathematical Society of Japan, Vol. 65, No. 4Homology of distributive latticesJózef H. Przytycki and Krzysztof K. Putyra11 August 2012 | Journal of Homotopy and Related Structures, Vol. 8, No. 1 Introductory Lectures on Knot TheoryMetrics History PDF download
Publication Year: 2011
Publication Date: 2011-09-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 62
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