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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Configuration spaces and $ \Theta_n$


Authors: David Ayala and Richard Hepworth
Journal: Proc. Amer. Math. Soc. 142 (2014), 2243-2254
MSC (2010): Primary 18D05, 55R80
Published electronically: April 11, 2014
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Abstract: We demonstrate that Joyal's category $ \Theta _n$, which is central to numerous definitions of $ (\infty ,n)$-categories, naturally encodes the homotopy type of configuration spaces of marked points in $ \mathbb{R}^n$. This article is largely self-contained and uses only elementary techniques in combinatorics and homotopy theory.


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Additional Information

David Ayala
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
Email: davidayala.math@gmail.com

Richard Hepworth
Affiliation: Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
Email: r.hepworth@abdn.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11946-0
PII: S 0002-9939(2014)11946-0
Received by editor(s): February 23, 2012
Received by editor(s) in revised form: July 16, 2012
Published electronically: April 11, 2014
Additional Notes: The work was supported by the Danish National Research Foundation (DNRF) through the Centre for Symmetry and Deformation
The first author was partially supported by ERC adv.grant No. 228082, and by the National Science Foundation under award No. 0902639
Communicated by: Brooke Shipley
Article copyright: © Copyright 2014 David Ayala and Richard Hepworth