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Journal Article
The Topology of Spaces of Knots: Cosimplicial Models
Dev P. Sinha
American Journal of Mathematics
Vol. 131, No. 4 (Aug., 2009), pp. 945-980
Published
by: The Johns Hopkins University Press
https://www.jstor.org/stable/40263760
Page Count: 36
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Topics: Vertices, Functors, Embeddings, Mathematical theorems, Algebraic topology, Mathematical manifolds, Partially ordered sets, Plant roots
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Abstract
We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial. These models build on the calculus of isotopy functors and are weakly homotopy equivalent to knot spaces when the ambient dimension is greater than three. The mapping space model, and the evaluation map on which it builds, is suitable for analysis through differential topology. The cosimplicial model gives rise to spectral sequences which converge to ohomology and homotopy groups of spaces of knots when they are connected. We explicitly identify and establish vanishing lines in these spectral sequences.
American Journal of Mathematics
© 2009 The Johns Hopkins University Press