Mathematical Research Letters

Volume 15 (2008)

Number 1

Coformality and rational homotopy groups of spaces of long knots

Pages: 1 – 15



Greg Arone (University of Virginia)

Pascal Lambrechts (Université Catholique de Louvain)

Victor Turchin (Université Catholique de Louvain)

Ismar Volić (Wellesley College)


We show that the Bousfield-Kan spectral sequence which computes the rational homotopy groups of the space of long knots in $\BR^d$ for $d\ge 4$ collapses at the $E^2$ page. The main ingredients in the proof are Sinha’s cosimplicial model for the space of long knots and a coformality result for the little balls operad.

Published 1 January 2008