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Cup-one algebras and $1$-minimal models

Richard D. Porter and Alexander I. Suciu

Algebraic & Geometric Topology 26 (2026) 65–134
Bibliography
1 A K Bousfield, D M Kan, Localization and completion in homotopy theory, Bull. Amer. Math. Soc. 77 (1971) 1006 MR296935
2 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR365573
3 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
4 P J Cahen, J L Chabert, Integer-valued polynomials, 48, Amer. Math. Soc. (1997) MR1421321
5 H Cartan, S Eilenberg, Homological algebra, Princeton Univ. Press (1956) MR77480
6 B Cenkl, R Porter, Nilmanifolds and associated Lie algebras over the integers, Pacific J. Math. 193 (2000) 5 MR1748179
7 S Eilenberg, S Mac Lane, On the groups H,n), I, Ann. of Math. (2) 58 (1953) 55 MR56295
8 T Ekedahl, On minimal models in integral homotopy theory, Homology Homotopy Appl. 4 (2002) 191 MR1918189
9 J Elliott, Binomial rings, integer-valued polynomials, and λ-rings, J. Pure Appl. Algebra 207 (2006) 165 MR2244389
10 Y Félix, S Halperin, J C Thomas, Rational homotopy theory, 205, Springer (2001) MR1802847
11 Y Félix, S Halperin, J C Thomas, Rational homotopy theory, II, World Scientific (2015) MR3379890
12 O. Flynn-Connolly, An obstruction theory for strictly commutative algebras in positive characteristic, preprint (2025) arXiv:2404.16681
13 R H Fox, On the Lusternik–Schnirelmann category, Ann. of Math. (2) 42 (1941) 333 MR4108
14 G Friedman, Survey article : an elementary illustrated introduction to simplicial sets, Rocky Mountain J. Math. 42 (2012) 353 MR2915498
15 N. Gadish, Letter-linking: bridging combinatorial group theory and topology, preprint (2025) arXiv:2308.13635
16 P Griffiths, J Morgan, Rational homotopy theory and differential forms, 16, Springer (2013) MR3136262
17 P Hall, The Edmonton notes on nilpotent groups, Queen Mary College, Mathematics Department (1969) MR283083
18 S Halperin, Lectures on minimal models, 9–10, Soc. Math. France (1983) 261 MR736299
19 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
20 G Hirsch, Quelques propriétés des produits de Steenrod, C. R. Acad. Sci. Paris 241 (1955) 923 MR73182
21 G Horel, Binomial rings and homotopy theory, J. Reine Angew. Math. 813 (2024) 283 MR4780987
22 T Kadeishvili, Cochain operations defining Steenrod i-products in the bar construction, Georgian Math. J. 10 (2003) 115 MR1990691
23 Y V Kuz’min, Y S Semenov, On the homology of a free nilpotent group of class 2, Mat. Sb. 189 (1998) 49 MR1632414
24 I Kříž, p-adic homotopy theory, Topology Appl. 52 (1993) 279 MR1243609
25 L A Lambe, S B Priddy, Cohomology of nilmanifolds and torsion-free, nilpotent groups, Trans. Amer. Math. Soc. 273 (1982) 39 MR664028
26 S MacLane, Homology, 114, Springer (1967) MR349792
27 A I Mal’cev, On a class of homogeneous spaces, Amer. Math. Soc. Translation 1951 (1951) 1 MR39734
28 M A Mandell, Cochains and homotopy type, Publ. Math. Inst. Hautes Études Sci. (2006) 213 MR2233853
29 J P May, Matric Massey products, J. Algebra 12 (1969) 533 MR238929
30 K Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. (2) 59 (1954) 531 MR64057
31 D Petersen, Cohomology of generalized configuration spaces, Compos. Math. 156 (2020) 251 MR4045070
32 R Porter, Milnor’s μ-invariants and Massey products, Trans. Amer. Math. Soc. 257 (1980) 39 MR549154
33 R D. Porter, A I. Suciu, Generalized Massey products, work in progress
34 R D Porter, A I Suciu, Homology, lower central series, and hyperplane arrangements, Eur. J. Math. 6 (2020) 1039 MR4151728
35 R D Porter, A I Suciu, Differential graded algebras, Steenrod cup-one products, binomial operations, and Massey products, Topology Appl. 313 (2022) 107987 MR4423095
36 R D. Porter, A I. Suciu, Groups associated to 1-minimal models for binomial cup-one algebras, preprint (2025)
37 B Richter, S Sagave, A strictly commutative model for the cochain algebra of a space, Compos. Math. 156 (2020) 1718 MR4163860
38 C P Rourke, B J Sanderson, Δ-sets, I : Homotopy theory, Quart. J. Math. Oxford Ser. (2) 22 (1971) 321 MR300281
39 N E Steenrod, Products of cocycles and extensions of mappings, Ann. of Math. (2) 48 (1947) 290 MR22071
40 A I Suciu, Formality and finiteness in rational homotopy theory, EMS Surv. Math. Sci. 10 (2023) 321 MR4667423
41 A I Suciu, H Wang, Formality properties of finitely generated groups and Lie algebras, Forum Math. 31 (2019) 867 MR3975666
42 D Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977) 269 MR646078
43 J H C Whitehead, On the homotopy type of ANR’s, Bull. Amer. Math. Soc. 54 (1948) 1133 MR29504
44 J H C Whitehead, Combinatorial homotopy, I, Bull. Amer. Math. Soc. 55 (1949) 213 MR30759