Coformality and the rational homotopy groups of spaces of long knots

Details Coformality and the rational homotopy groups of spaces of long knots Coformality and the rational homotopy groups of spaces of long knots

2007-01-12

arxiv.org/abs/math/0701350v3

Mathematics

Algebraic Topology

12 pages. Revised (and presumably final) version. Accepted for publication in Mathematical Research Letters

Scientific paper

We show that the Bousfield-Kan spectral sequence which computes the rational
homotopy groups of the space of long knots in ${\mathbb R}^d$, where $d\ge 4$,
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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