Geodesic
The space of short ropes and the classifying space of the space of long knots
Moriya, Syunji1 ; Sakai, Keiichi2
1 Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Japan
2 Department of Mathematical Sciences, Shinshu University, Asahi, Matsumoto, Japan
Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2859-2873

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove affirmatively the conjecture raised by J Mostovoy (Topology 41 (2002) 435–450); the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in ℝ3. We make use of techniques developed by S Galatius and O Randal-Williams (Geom. Topol. 14 (2010) 1243–1302) 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.

DOI : 10.2140/agt.2018.18.2859
Classification : 57R19, 55R35, 57M25
Keywords: topological category of long knots, the space of short ropes, classifying space, group completions, spaces of manifolds

Moriya, Syunji 1 ; Sakai, Keiichi 2

1 Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Japan
2 Department of Mathematical Sciences, Shinshu University, Asahi, Matsumoto, Japan 
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Moriya, Syunji; Sakai, Keiichi. The space of short ropes and the classifying space of the space of long knots. Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2859-2873. doi: 10.2140/agt.2018.18.2859

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