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arXiv · 1610.03907

The space of short ropes and the classifying space of the space of long knots

Syunji Moriya·Keiichi Sakai
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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 $\mathbb{R}^3$. 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.

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Syunji Moriya, Keiichi Sakai. 2016-10-13. The space of short ropes and the classifying space of the space of long knots. https://doi.org/10.2140/agt.2018.18.2859

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