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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Configuration spaces and $\Theta _n$
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by David Ayala and Richard Hepworth PDF
Proc. Amer. Math. Soc. 142 (2014), 2243-2254

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.
References
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Additional Information
  • David Ayala
  • Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
  • MR Author ID: 810829
  • 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
  • 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
  • © Copyright 2014 David Ayala and Richard Hepworth
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2243-2254
  • MSC (2010): Primary 18D05, 55R80
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11946-0
  • MathSciNet review: 3195750