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A one-dimensional embedding complex

Kevin P. Scannell·Dev P. Sinha
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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.

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Kevin P. Scannell, Dev P. Sinha. 2000-11-02. A one-dimensional embedding complex. https://arxiv.org/abs/math/0011020

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