Coformality and the rational homotopy groups of spaces of long knots

2007/01/12 by Gregory Arone, Arone, Gregory, Pascal Lambrechts +5
Mathematics · #57Q45 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0701350

openalex publication_date 2007/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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≥ 4, collapses at the E² 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.

Cited by

• Calculus of functors, operad formality, and rational homology of embedding spaces

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