Volume 23, issue 1 (2019)

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

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
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
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
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