Title: The topology of spaces of knots.
Author: Dev P. Sinha
AMS Class: 57R40 (primary); 55T35, 57Q45 (secondary).
LANL ID: math.AT/0202287
Addresses: Department of Mathematics, University of Oregon, Eugene OR and
Department of Mathematics, Brown University, Providence RI
Email: dps@math.brown.edu
Included EPS files: smallpenta.eps, smalltreepenta.eps
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 mapping spaces and another which is cosimplicial. These
models are homotopy equivalent to the corresponding knot spaces when the
dimension of the ambient manifold is greater than three, and there are
spectral sequences with identifiable $E^1$ terms which converge to their
cohomology and homotopy groups. The combinatorics of the spectral
sequences is comparable to combinatorics which arises in finite-type
invariant theory.