English

A one-dimensional embedding complex

Algebraic Topology 2007-05-23 v1 Geometric Topology Quantum Algebra

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 E^1 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 E^1 term is zero, and make calculations of E^2 in a finite range.

Keywords

Cite

@article{arxiv.math/0011020,
  title  = {A one-dimensional embedding complex},
  author = {Kevin P. Scannell and Dev P. Sinha},
  journal= {arXiv preprint arXiv:math/0011020},
  year   = {2007}
}

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11 pages