A one-dimensional embedding complex

✍ Scribed by Kevin P. Scannell; Dev P. Sinha

• Book ID: 104152454
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 137 KB
• Volume: 170
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00078-0

✦ Synopsis

We give the ÿrst explicit computations of rational homotopy groups of spaces of "long knots" in Euclidean spaces. We deÿne a spectral sequence which converges to these rational homotopy groups whose E 1 term is deÿned in terms of familiar 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 ÿnite range.