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2014 On the rational homology of high-dimensional analogues of spaces of long knots
Gregory Arone, Victor Turchin
Geom. Topol. 18(3): 1261-1322 (2014). DOI: 10.2140/gt.2014.18.1261


We study high-dimensional analogues of spaces of long knots. These are spaces of compactly supported embeddings (modulo immersions) of m into n. We view the space of embeddings as the value of a certain functor at m, and we apply manifold calculus to this functor. Our first result says that the Taylor tower of this functor can be expressed as the space of maps between infinitesimal bimodules over the little-disks operad. We then show that the formality of the little-disks operad has implications for the homological behavior of the Taylor tower. Our second result says that when 2m+1<n, the singular chain complex of these spaces of embeddings is rationally equivalent to a direct sum of certain finite chain complexes, which we describe rather explicitly.


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Gregory Arone. Victor Turchin. "On the rational homology of high-dimensional analogues of spaces of long knots." Geom. Topol. 18 (3) 1261 - 1322, 2014.


Received: 29 March 2012; Revised: 14 October 2013; Accepted: 24 December 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1312.57034
MathSciNet: MR3228453
Digital Object Identifier: 10.2140/gt.2014.18.1261

Primary: 57R70
Secondary: 18D50 , 18G55

Keywords: embedding spaces , formality , infinitesimal bimodules

Rights: Copyright © 2014 Mathematical Sciences Publishers

Vol.18 • No. 3 • 2014
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