Volume 23, issue 1 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Operads of genus zero curves and the Grothendieck–Teichmüller group

Pedro Boavida de Brito, Geoffroy Horel and Marcy Robertson

Geometry & Topology 23 (2019) 299–346
Bibliography
1 D W Anderson, Fibrations and geometric realizations, Bull. Amer. Math. Soc. 84 (1978) 765 MR0500935
2 I Barnea, Y Harpaz, G Horel, Pro-categories in homotopy theory, Algebr. Geom. Topol. 17 (2017) 567 MR3604386
3 G V Belyĭ, On Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979) 267 MR534593
4 C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
5 C Berger, I Moerdijk, Resolution of coloured operads and rectification of homotopy algebras, from: "Categories in algebra, geometry and mathematical physics" (editors A Davydov, M Batanin, M Johnson, S Lack, A Neeman), Contemp. Math. 431, Amer. Math. Soc. (2007) 31 MR2342815
6 J E Bergner, P Hackney, Group actions on Segal operads, Israel J. Math. 202 (2014) 423 MR3265328
7 D C Cisinski, I Moerdijk, Dendroidal Segal spaces and –operads, J. Topol. 6 (2013) 675 MR3100887
8 V G Drinfeld, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(), Algebra i Analiz 2 (1990) 149 MR1080203
9 G C Drummond-Cole, Homotopically trivializing the circle in the framed little disks, J. Topol. 7 (2014) 641 MR3252959
10 W G Dwyer, D M Kan, Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980) 17 MR578563
11 W G Dwyer, D M Kan, Function complexes in homotopical algebra, Topology 19 (1980) 427 MR584566
12 B Fresse, Homotopy of operads and Grothendieck–Teichmüller groups, I : The algebraic theory and its topological background, 217, Amer. Math. Soc. (2017) MR3643404
13 E Getzler, Batalin–Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (1994) 265 MR1256989
14 E Getzler, Operads and moduli spaces of genus 0 Riemann surfaces, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 199 MR1363058
15 J Giansiracusa, P Salvatore, Formality of the framed little 2–discs operad and semidirect products, from: "Homotopy theory of function spaces and related topics" (editors Y Félix, G Lupton, S B Smith), Contemp. Math. 519, Amer. Math. Soc. (2010) 115 MR2648708
16 A Grothendieck, Esquisse d’un programme, from: "Geometric Galois actions, I" (editors L Schneps, P Lochak), London Math. Soc. Lecture Note Ser. 242, Cambridge Univ. Press (1997) 5 MR1483107
17 F Guillén Santos, V Navarro, P Pascual, A Roig, Moduli spaces and formal operads, Duke Math. J. 129 (2005) 291 MR2165544
18 A Hatcher, P Lochak, L Schneps, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. 521 (2000) 1 MR1752293
19 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
20 G Horel, Profinite completion of operads and the Grothendieck–Teichmüller group, Adv. Math. 321 (2017) 326 MR3715714
21 D C Isaksen, A model structure on the category of pro-simplicial sets, Trans. Amer. Math. Soc. 353 (2001) 2805 MR1828474
22 P T Johnstone, Stone spaces, 3, Cambridge Univ. Press (1982) MR698074
23 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
24 I Moerdijk, I Weiss, Dendroidal sets, Algebr. Geom. Topol. 7 (2007) 1441 MR2366165
25 D Petersen, Minimal models, GT–action and formality of the little disk operad, Selecta Math. 20 (2014) 817 MR3217461
26 G Quick, Profinite homotopy theory, Doc. Math. 13 (2008) 585 MR2466189
27 G Quick, Some remarks on profinite completion of spaces, from: "Galois–Teichmüller theory and arithmetic geometry" (editors H Nakamura, F Pop, L Schneps, A Tamagawa), Adv. Stud. Pure Math. 63, Math. Soc. Japan (2012) 413 MR3051250
28 D Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. 100 (1974) 1 MR0442930
29 U Tillmann, Higher genus surface operad detects infinite loop spaces, Math. Ann. 317 (2000) 613 MR1776120
30 P Ševera, Formality of the chain operad of framed little disks, Lett. Math. Phys. 93 (2010) 29 MR2661521
31 N Wahl, Ribbon braids and related operads, PhD thesis, Oxford University (2001)
32 N Wahl, Infinite loop space structure(s) on the stable mapping class group, Topology 43 (2004) 343 MR2052967