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.
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}
}
Comments
11 pages