A one-dimensional embedding complex |
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Authors: | Kevin P Scannell Dev P Sinha |
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Institution: | a Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, USA b Department of Mathematics, Brown University, Providence, RI 02906, USA |
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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 E1 term is defined 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 E1 term is zero, and make calculations of E2 in a finite range. |
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Keywords: | Primary: 57R40 secondary: 55T99 17B70 57M25 57M27 55R80 |
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