Translator Disclaimer
2018 The space of short ropes and the classifying space of the space of long knots
Syunji Moriya, Keiichi Sakai
Algebr. Geom. Topol. 18(5): 2859-2873 (2018). DOI: 10.2140/agt.2018.18.2859

Abstract

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 3 . 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.

Citation

Download Citation

Syunji Moriya. Keiichi Sakai. "The space of short ropes and the classifying space of the space of long knots." Algebr. Geom. Topol. 18 (5) 2859 - 2873, 2018. https://doi.org/10.2140/agt.2018.18.2859

Information

Received: 29 May 2017; Revised: 24 January 2018; Accepted: 22 February 2018; Published: 2018
First available in Project Euclid: 30 August 2018

zbMATH: 06935822
MathSciNet: MR3848401
Digital Object Identifier: 10.2140/agt.2018.18.2859

Subjects:
Primary: 57R19
Secondary: 55R35, 57M25

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.18 • No. 5 • 2018
MSP
Back to Top