| Title:
|
Configuration spaces form a Segal semi-dendroidal space (English) |
| Author:
|
Hackney, Philip |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
2 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
234-240 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Dendroidal set |
| Keyword:
|
configuration space |
| Keyword:
|
presheaf |
| MSC:
|
18D50 |
| MSC:
|
18G30 |
| MSC:
|
55P48 |
| MSC:
|
55R80 |
| idZBL:
|
Zbl 1409.55007 |
| idMR:
|
MR3917430 |
| DOI:
|
10.21136/HS.2018.07 |
| . |
| Date available:
|
2026-03-10T17:55:39Z |
| Last updated:
|
2026-03-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153406 |
| . |
| Reference:
|
[1] Berger, Clemens, Moerdijk, Ieke: On an extension of the notion of Reedy category.Math. Z. 269, no. 3-4, 977–1004 10.1007/s00209-010-0770-x |
| Reference:
|
[2] Bergner, Julia E., Hackney, Philip: Group actions on Segal operads.Israel J. Math. 202, no. 1, 423–460 10.1007/s11856-014-1075-2 |
| Reference:
|
[3] Cisinski, Denis-Charles, Moerdijk, Ieke: Dendroidal sets and simplicial operads.J. Topol. 6, no. 3, 705–756 10.1112/jtopol/jtt006 |
| Reference:
|
[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 |
| Reference:
|
[5] Moerdijk, Ieke, Weiss, Ittay: Dendroidal sets.Algebr. Geom. Topol. 7, 1441–1470 10.2140/agt.2007.7.1441 |
| . |
