Abstract
Racks were introduced in [FR]. In this paper we define a natural category like object, called a species.* A particularly important species is associated with a rack. A species has a nerve, analogous to the nerve of a category, and the nerve of the rack species yields a space associated to the rack which classifies link diagrams labelled by the rack. We compute the second homotopy group of this space in the case of a classical rack. This is a free abelian group of rank the number of non-trivial maximal irreducible sublinks of the link.
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© 1993 Springer Science+Business Media Dordrecht
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Fenn, R., Rourke, C., Sanderson, B. (1993). An Introduction to Species and the Rack Space. In: Bozhüyük, M.E. (eds) Topics in Knot Theory. NATO ASI Series, vol 399. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1695-4_4
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DOI: https://doi.org/10.1007/978-94-011-1695-4_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4742-5
Online ISBN: 978-94-011-1695-4
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