A one-dimensional embedding complex

Published in Journal of Pure and Applied Algebra, 2002

Recommended citation: Kevin P. Scannell and Dev P. Sinha. A one-dimensional embedding complex. Journal of Pure and Applied Algebra, 170(1):93–107, 2002. https://kevinscannell.com/files/jpaa.pdf

DOI: doi:10.1016/S0022-4049(01)00078-0

Abstract: 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 E1 term is defined in terms of familiar Lie algebras. For odd k we establish a vanishing line for this spectral sequence, show the Euler characteristic of the rows of this E1 term is zero, and make calculations of E2 in a finite range.