The topology of spaces of knots: cosimplicial models

By Dev Sinha. 2002

61 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9a2fc3c44420d001c490767a8037117616014266

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the rational homology of high dimensional analogues of spaces of long knots (2011, background): “1 is related to Sinha’s cosimplicial model for the space of long knots [22].”
Cubical Homotopy Theory (2015, methodology): “Many of the definitions and results in this section first appeared in [Sin09], with some expansions, details, and proofs that did not exist in the literature provided in [MV14].”
Hodge‐type decomposition in the homology of long knots (2010, methodology): “Cosimplicial model for Embd For any d 4, Sinha defined a cosimplicial model Cd• = {Cd |n 0}, whose homotopy totalization is weakly homotopy equivalent to Embd (see [35]).”