  This paper gives a partial description of the homotopy type of K, the space
of long knots in 3-dimensional Euclidean space. The primary result is the
construction of a homotopy equivalence between K and the free little 2-cubes
object over the space of prime knots. In proving the freeness result, a close
correspondence is discovered between the Jaco-Shalen-Johannson decomposition of
knot complements and the little cubes action on K. Beyond studying long knots
in 3-space, we show that for any compact manifold M the space of embeddings of
R^n x M in R^n x M with support in I^n x M admits an action of the operad of
little (n+1)-cubes. If M=D^k this embedding space is the space of framed long
n-knots in R^{n+k}, and the action of the little cubes operad is an enrichment
of the monoid structure given by the connected-sum operation.
