Mathematical Research Letters
Volume 15, Issue 1, January 2008 pp. 1-15.
Coformality and rational homotopy groups of spaces of long knotsAuthors: Greg Arone (1), Pascal Lambrechts (2), Victor Turchin (3) and Ismar Volić (4)
Author institution: University of Virginia (1), Université Catholique de Louvain (2), Université Catholique de Louvain (3), and Wellesley College (4)
Summary: 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.
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