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

23 Mar 2018 Moriya Syunji Sakai Keiichi

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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Categories


  • ALGEBRAIC TOPOLOGY
  • GEOMETRIC TOPOLOGY