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The Deligne–Mumford operad as a trivialization of the circle action

Alexandru Oancea and Dmitry Vaintrob

Algebraic & Geometric Topology 26 (2026) 1229–1291
DOI: 10.2140/agt.2026.26.1229
Bibliography
1 M Abouzaid, A geometric criterion for generating the Fukaya category, Publ. Math. Inst. Hautes Études Sci. 112 (2010) 191 MR2737980
2 M Abouzaid, Y Groman, U Varolgunes, Framed E2 structures in Floer theory, Adv. Math. 450 (2024) 109755 MR4756849
3 n authors, proper model category, (2024)
4 n authors, Strøm model structure, (2024)
5 C Barwick, From operator categories to higher operads, Geom. Topol. 22 (2018) 1893 MR3784514
6 C Berger, B Fresse, Combinatorial operad actions on cochains, Math. Proc. Cambridge Philos. Soc. 137 (2004) 135 MR2075046
7 C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
8 C Berger, I Moerdijk, The Boardman–Vogt resolution of operads in monoidal model categories, Topology 45 (2006) 807 MR2248514
9 P Candelas, X C de la Ossa, P S Green, L Parkes, A pair of Calabi–Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991) 21 MR1115626
10 H Chu, R Haugseng, G Heuts, Two models for the homotopy theory of -operads, J. Topol. 11 (2018) 857 MR3847208
11 D C Cisinski, I Moerdijk, Dendroidal Segal spaces and -operads, J. Topol. 6 (2013) 675 MR3100887
12 D C Cisinski, I Moerdijk, Dendroidal sets and simplicial operads, J. Topol. 6 (2013) 705 MR3100888
13 M Cole, Mixing model structures, Topology Appl. 153 (2006) 1016 MR2203016
14 K J Costello, The Gromov–Witten potential associated to a TCFT, (2005) arXiv:math/0509264
15 K Costello, The partition function of a topological field theory, J. Topol. 2 (2009) 779 MR2574744
16 D A Cox, S Katz, Mirror symmetry and algebraic geometry, 68, Amer. Math. Soc. (1999) MR1677117
17 A Căldăraru, K Costello, J Tu, Categorical enumerative invariants, I : String vertices, (2020) arXiv:2009.06673
18 A Căldăraru, J Tu, Categorical enumerative invariants, II: Givental formula, (2025) arXiv:2009.06659
19 Y Deshmukh, A homotopical description of Deligne–Mumford compactifications, (2022) arXiv:2211.05168
20 V Dotsenko, S Shadrin, B Vallette, Givental action and trivialisation of circle action, J. Éc. polytech. Math. 2 (2015) 213 MR3426748
21 G C Drummond-Cole, Homotopically trivializing the circle in the framed little disks, J. Topol. 7 (2014) 641 MR3252959
22 G C Drummond-Cole, B Vallette, The minimal model for the Batalin–Vilkovisky operad, Selecta Math. (N.S.) 19 (2013) 1 MR3029946
23 W G Dwyer, D M Kan, Homotopy theory and simplicial groupoids, Nederl. Akad. Wetensch. Indag. Math. 46 (1984) 379 MR770723
24 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
25 S Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, PhD thesis, Massachusetts Institute of Technology (2012) MR3121862
26 G Ginot, Introduction à l’homotopie, lecture notes (2018–2019)
27 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
28 J Harris, I Morrison, Moduli of curves, 187, Springer (1998) MR1631825
29 G Heuts, V Hinich, I Moerdijk, On the equivalence between Lurie’s model and the dendroidal model for infinity-operads, Adv. Math. 302 (2016) 869 MR3545944
30 G Heuts, I Moerdijk, Simplicial and dendroidal homotopy theory, 75, Springer (2022) MR4485749
31 V Hinich, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997) 3291 MR1465117
32 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
33 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
34 P T Johnstone, Sketches of an elephant: a topos theory compendium, I, 43, Oxford Univ. Press (2002) MR1953060
35 A Khoroshkin, N Markarian, S Shadrin, Hypercommutative operad as a homotopy quotient of BV, Comm. Math. Phys. 322 (2013) 697 MR3079329
36 J Kock, Polynomial functors and trees, Int. Math. Res. Not. 2011 (2011) 609 MR2764874
37 M Kontsevich, Homological algebra of mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, I" (editor S D Chatterji), Birkhäuser (1995) 120 MR1403918
38 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
39 M Kontsevich, Y Soibelman, Deformations of algebras over operads and the Deligne conjecture, from: "Conférence Moshé Flato, I" (editors G Dito, D Sternheimer), Math. Phys. Stud. 21, Kluwer Acad. (2000) 255 MR1805894
40 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
41 J Lurie, Higher algebra, preprint (2017)
42 M Markl, S Shnider, J Stasheff, Operads in algebra, topology and physics, 96, Amer. Math. Soc. (2002) MR1898414
43 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR420610
44 J P May, A concise course in algebraic topology, University of Chicago Press (1999) MR1702278
45 J P May, K Ponto, More concise algebraic topology: localization, completion, and model categories, University of Chicago Press (2012) MR2884233
46 J E McClure, J H Smith, A solution of Deligne’s Hochschild cohomology conjecture, from: "Recent progress in homotopy theory" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 153 MR1890736
47 I Moerdijk, I Weiss, Dendroidal sets, Algebr. Geom. Topol. 7 (2007) 1441 MR2366165
48 B Noohi, Foundations of topological stacks, I, (2005) arXiv:0503247
49 D G Quillen, Homotopical algebra, 43, Springer (1967) MR223432
50 D Quillen, Higher algebraic K-theory, I, from: "Algebraic K-theory, I : Higher K-theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85 MR338129
51 F Schottky, Ueber die conforme Abbildung mehrfach zusammenhängender ebener Flächen, J. Reine Angew. Math. 83 (1877) 300 MR1579739
52 N Strickland, The category of CGWH spaces, (2009)
53 A Strøm, The homotopy category is a homotopy category, Arch. Math. (Basel) 23 (1972) 435 MR321082
54 D E Tamarkin, Another proof of M. Kontsevich formality theorem, (1998) arXiv:math/9803025
55 J Tu, Categorical enumerative invariants of the ground field, (2021) arXiv:2103.01383
56 D Vaintrob, Moduli of framed formal curves, (2019) arXiv:1910.11550
57 A Vistoli, Grothendieck topologies, fibered categories and descent theory, from: "Fundamental algebraic geometry", Math. Surveys Monogr. 123, Amer. Math. Soc. (2005) 1 MR2223406
58 R M Vogt, Cofibrant operads and universal E operads, Topology Appl. 133 (2003) 69 MR1996461
59 A A Voronov, Homotopy Gerstenhaber algebras, from: "Conférence Moshé Flato, II" (editors G Dito, D Sternheimer), Math. Phys. Stud. 22, Kluwer Acad. (2000) 307 MR1805923
60 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324