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Keywords:
Dendroidal set; configuration space; presheaf
Dendroidal set; configuration space; presheaf
Summary:
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.
References:
[1] Berger, Clemens, Moerdijk, Ieke: On an extension of the notion of Reedy category. Math. Z. 269, no. 3-4, 977–1004 DOI 10.1007/s00209-010-0770-x
[2] Bergner, Julia E., Hackney, Philip: Group actions on Segal operads. Israel J. Math. 202, no. 1, 423–460 DOI 10.1007/s11856-014-1075-2
[3] Cisinski, Denis-Charles, Moerdijk, Ieke: Dendroidal sets and simplicial operads. J. Topol. 6, no. 3, 705–756 DOI 10.1112/jtopol/jtt006
[4] Moerdijk, Ieke: Lectures on dendroidal sets. Simplicial methods for operads and algebraic geometry, Adv. Courses Math. CRM Barcelona, Birkhäuser/Springer Basel AG, Basel, Notes written by Javier J. Gutiérrez, pp. 1–118
[5] Moerdijk, Ieke, Weiss, Ittay: Dendroidal sets. Algebr. Geom. Topol. 7, 1441–1470 DOI 10.2140/agt.2007.7.1441
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