  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
(defined in [Trunks and classifying spaces, Applied Categorical Structures, 3
(1995) 321--356]) and the classifying bundle is the first James bundle (defined
in "James bundles" math.AT/0301354).
  We investigate the algebraic topology of this classifying space and report on
calculations given elsewhere. Apart from defining 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.
