The rack space

By R. Fenn, Colin Rourke, Brian Sanderson. 2003

87 citations recorded by the source corpus.

The main result of this paper is a new classification theorem for links (smooth embeddings in codimension 2). The classifying space is the rack space and the classifying bundle is the first James bundle. We investigate the algebraic topology of this classifying space and report on calculations given elsewhere. Apart from de. ning many new knot and link invariants (including generalised James-Hopf invariants), the classification theorem has some unexpected applications. We give a combinatorial interpretation for pi(2) of a complex which can be used for calculations and some new interpretations of the higher homotopy groups of the 3-sphere. We also give a cobordism classification of virtual links.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28df8aa0567df9e3bfe309b6f88beb2d80df6a1d

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In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homology Groups of Symmetric Quandles and Cocycle Invariants of Links and Surface-links (2009, background): “For details on quandle homologies and invariants, refer to [1, 3, 4, 5, 10, 11, 16, 20, 21].”
Yang–Baxter deformations of quandles and racks (2004, background): “tors to diagonal matrices, that is, to matrices f: Qn×Qn →m with f[x1,...,xn y1,...,yn ] = 0 whenever xi6= yi for some i. In this case we obtain the cochain complex of quandle or rack cohomology (see [6, 9, 15]). 3.2 Characterization of entropic maps Recall from Deﬁnition 10 that a map f: AQn→mQn is”
What is a virtual link (2002, background): “o [1]. They show that virtual links are equivalent to stable equivalence classes of links projections onto compact, oriented surfaces. (Fenn, Rourke, and Sanderson have written a self-contained proof [2].) The surface S need not be connected, but we require that each component contains at least one ”