Higher Structures, Vol. 2, No. 1, pp. 234-240, 2018

Configuration spaces form a Segal semi-dendroidal space

Philip Hackney

Received August 16th 2017. Published online November 8th 2018.

Abstract:  The purpose of this short note is to illustrate the utility of (semi-) dendroidal objects in describing certain ‘up-to-homotopy’ operads. Specifically, we exhibit a semi-dendroidal space satisfying the Segal condition, whose evaluation at a $k$-corolla is the space of ordered configurations of $k$ points in the $n$-dimensional unit ball.
Keywords:  Dendroidal set; configuration space; presheaf
Classification MSC:  55R80, 55P48, 18G30, 18D50

PDF available at:  Institute of Mathematics CAS

Affiliations:   Philip Hackney, Department of Mathematics, Macquarie University, NSW, Australia Current Address: Department of Mathematics, University of Louisiana at Lafayette, LA, USA, e-mail: philip@phck.net

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