I am doing project in Quandles . And I am reading Thesis by David joyce An Algebraic Approach to Symmetry with Applications to Knot Theory . In its Section 4.5 Knot quandles page number 46 there is a line " when a loop in X-K links once with K " , I am not getting what it means . And after that knot quandle is defined as nooses linking once with K upto homotopy which is also not clear to me . I have not done course in Algebraic topology and knot theory but I have read fundamental groups myself . If possible please explain through figure.
Any type of help will be appreciated.
http://repository.upenn.edu/cgi/viewcontent.cgi?article=2110&context=edissertations
This is an excellent question.
For an introduction to knot quandles, see
A classifying invariant of knots, the knot quandle
https://www.researchgate.net/publication/222157351_A_classifying_invariant_of_knots_the_knot_quandle
See, also:
FOUNDATIONS OF TOPOLOGICAL RACKS AND QUANDLES
https://arxiv.org/pdf/1506.00084.pdf
GENERATING SETS OF REIDEMEISTER MOVES OF ORIENTED
SINGULAR LINKS AND QUANDLES
https://www.researchgate.net/profile/Khaled_Bataineh2/publication/313397530_Generating_sets_of_Reidemeister_moves_of_oriented_singular_links_and_quandles/links/589b9140aca2721ae1b7a3b6/Generating-sets-of-Reidemeister-moves-of-oriented-singular-links-and-quandles.pdf?origin=publication_detail
Article A classifying invariant of knots, the knot quandle
Article Generating sets of Reidemeister moves of oriented singular l...
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