Algebraic & Geometric Topology Volume 25, issue 9 (2025)

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ISSN (print): 1472-2747

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Loop homology of moment-angle complexes in the flag case

Fedor Vylegzhanin

Algebraic & Geometric Topology 25 (2025) 5619–5663

DOI: 10.2140/agt.2025.25.5619

Bibliography

1	S Amelotte, Connected sums of sphere products and minimally non-Golod complexes, from: "Toric topology and polyhedral products" (editors A Bahri, L Jeffrey, T Panov, D Stanley, S Theriault), Fields Inst. Commun. 89, Springer (2024) 1 MR4789589
2	N Andruskiewitsch, J Devoto, Extensions of Hopf algebras, Algebra i Analiz 7 (1995) 22 MR1334152
3	D Anick, W Dicks, A mnemonic for the graded-case Golod–Shafarevich inequality, preprint (2015) arXiv:1508.03231
4	L L Avramov, Infinite free resolutions, from: "Six lectures on commutative algebra", Progr. Math. 166, Birkhäuser (1998) 1 MR1648664
5	A Bahri, M Bendersky, F R Cohen, Polyhedral products and features of their homotopy theory, from: "Handbook of homotopy theory" (editor H Miller), CRC Press (2020) 103 MR4197983
6	I V Baskakov, Triple Massey products in the cohomology of moment-angle complexes, Uspekhi Mat. Nauk 58 (2003) 199 MR2035723
7	S Basu, A Bhowmick, S Samanta, On the James brace product : generalization, relation to H-splitting of loop space fibrations & the J-homomorphism, preprint (2024) arXiv:2401.16206
8	H J Baues, The double bar and cobar constructions, Compositio Math. 43 (1981) 331 MR632433
9	P Beben, S Theriault, Homotopy groups of highly connected Poincaré duality complexes, Doc. Math. 27 (2022) 183 MR4398609
10	A Berglund, Koszul spaces, Trans. Amer. Math. Soc. 366 (2014) 4551 MR3217692
11	W Browder, On differential Hopf algebras, Trans. Amer. Math. Soc. 107 (1963) 153 MR145530
12	G Brumfiel, J Morgan, Explicit acyclic models and (co)chain operations, preprint (2023) arXiv:2310.03729
13	V Buchstaber, J Grbić, Hopf algebras and homology of loop suspension spaces, from: "Topology, geometry, integrable systems, and mathematical physics" (editors V M Buchstaber, B A Dubrovin, I M Krichever), Amer. Math. Soc. Transl. Ser. 2 234, Amer. Math. Soc. (2014) 75 MR3307144
14	V M Buchstaber, I Y Limonchenko, Massey products, toric topology and combinatorics of polytopes, Izv. Math. 83 (2019) 1081 MR4036750
15	V M Buchstaber, T E Panov, Toric topology, 204, Amer. Math. Soc. (2015) MR3363157
16	L Cai, On the graph products of simplicial groups and connected Hopf algebras, J. Algebra 647 (2024) 99 MR4714761
17	B Eckmann, P J Hilton, Operators and cooperators in homotopy theory, Math. Ann. 141 (1960) 1 MR115162
18	Y Félix, S Halperin, J C Thomas, Adams’ cobar equivalence, Trans. Amer. Math. Soc. 329 (1992) 531 MR1036001
19	M Franz, The cohomology rings of smooth toric varieties and quotients of moment-angle complexes, Geom. Topol. 25 (2021) 2109 MR4286370
20	M Franz, Homotopy Gerstenhaber formality of Davis–Januszkiewicz spaces, Homology Homotopy Appl. 23 (2021) 325 MR4317573
21	R Fröberg, Determination of a class of Poincaré series, Math. Scand. 37 (1975) 29 MR404254
22	R Fröberg, Koszul algebras, from: "Advances in commutative ring theory", Lecture Notes in Pure and Appl. Math. 205, Dekker (1999) 337 MR1767430
23	J Grbić, T Panov, S Theriault, J Wu, The homotopy types of moment-angle complexes for flag complexes, Trans. Amer. Math. Soc. 368 (2016) 6663 MR3461047
24	J Grbić, G Simmons, M Ilyasova, T Panov, One-relator groups and algebras related to polyhedral products, Proc. Roy. Soc. Edinburgh Sect. A 152 (2022) 128 MR4383244
25	S Halperin, Universal enveloping algebras and loop space homology, J. Pure Appl. Algebra 83 (1992) 237 MR1194839
26	R Huang, Coformality around fibrations and cofibrations, Homology Homotopy Appl. 25 (2023) 235 MR4590324
27	I M James, Reduced product spaces, Ann. of Math. 62 (1955) 170 MR73181
28	S Mac Lane, Homology, Springer (1995)
29	J M Lemaire, Algèbres connexes et homologie des espaces de lacets, 422, Springer (1974) MR370566
30	C C Li, G S Zhou, The structure of connected (graded) Hopf algebras revisited, J. Algebra 610 (2022) 684 MR4469128
31	J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. 81 (1965) 211 MR174052
32	J Neisendorfer, Algebraic methods in unstable homotopy theory, 12, Cambridge Univ. Press (2010) MR2604913
33	J A Neisendorfer, What is loop multiplication anyhow?, J. Homotopy Relat. Struct. 12 (2017) 659 MR3691300
34	D Notbohm, N Ray, On Davis–Januszkiewicz homotopy types, I : Formality and rationalisation, Algebr. Geom. Topol. 5 (2005) 31 MR2135544
35	T E Panov, N Ray, Categorical aspects of toric topology, from: "Toric topology", Contemp. Math. 460, Amer. Math. Soc. (2008) 293 MR2428364
36	S B Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970) 39 MR265437
37	J J Rotman, An introduction to homological algebra, Springer (2009) MR2455920
38	B Saleh, Noncommutative formality implies commutative and Lie formality, Algebr. Geom. Topol. 17 (2017) 2523 MR3686405
39	L Stanton, Loop space decompositions of moment-angle complexes associated to flag complexes, Q. J. Math. 75 (2024) 457 MR4765779
40	S Theriault, Toric homotopy theory, from: "Combinatorial and toric homotopy" (editors A Darby, J Grbić, Z Lü, J Wu), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 35, World Sci. (2018) 1 MR3792460
41	S Theriault, Homotopy fibrations with a section after looping, 1499 (2024) MR4790259
42	Y A Verevkin, Pontryagin algebras of some moment-angle complexes, Dal’nevost. Mat. Zh. 16 (2016) 9 MR3606988
43	F E Vylegzhanin, Pontryagin algebras and the LS-category of moment-angle complexes in the flag case, Proc. Steklov Inst. Math. 317 (2022) 55 MR4538823
44	C T C Wall, Generators and relations for the Steenrod algebra, Ann. of Math. 72 (1960) 429 MR116326