The space of short ropes and the classifying space of the space of long knots
arXiv:1610.03907 · doi:10.2140/agt.2018.18.2859
Abstract
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in . We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way.
10 pages, 5 figures, to appear in Algebraic and Geometric Topology