A one-dimensional embedding complex
by Kevin P. Scannell and Dev P. Sinha
St. Louis University and Brown University
scannell@slu.edu dps@math.brown.edu
We give the first explicit computations of rational homotopy groups of
spaces of "long knots" in Euclidean spaces. We define a spectral
sequence which converges to these rational homotopy groups whose E^1
term is defined in terms of Lie algebras related to braid groups. For
odd k we establish a vanishing line for this spectral sequence, show the
Euler characteristic of the rows of this E^1 term is zero, and make
calculations of E^2 in a finite range.