A one-dimensional embedding complex

2000/11/02 by Kevin P. Scannell, Scannell, Kevin P., Dev P. Sinha +1 · 1 citation
Mathematics · #57R40 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.AT #math.GT #math.QA #msc:57R40

paper · pdf · doi:10.48550/arxiv.math/0011020

11 pages

arxiv created 2000/11/02 · arxiv updated 2009/11/30

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 braid 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.

Cited by

• Embedding calculus and Vassiliev spectral sequence

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