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Higher homotopy invariants for spaces and maps

David Blanc, Mark W Johnson and James M Turner

Algebraic & Geometric Topology 21 (2021) 2425–2488
Bibliography
1 J F Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960) 20 MR141119
2 J F Adams, Algebraic topology : a student’s guide, 4, Cambridge Univ. Press (1972) MR0445484
3 S Basu, D Blanc, D Sen, Note on Toda brackets, J. Homotopy Relat. Struct. 15 (2020) 495 MR4182882
4 S Basu, D Blanc, D Sen, Higher structure in the unstable Adams spectral sequence, Homology Homotopy Appl. 23 (2021) 69 MR4242740
5 H J Baues, D Blanc, S Gondhali, Higher Toda brackets and Massey products, J. Homotopy Relat. Struct. 11 (2016) 643 MR3578993
6 H J Baues, M Jibladze, Suspension and loop objects in theories and cohomology, Georgian Math. J. 8 (2001) 697 MR1884494
7 D A Blanc, A Hurewicz spectral sequence for homology, Trans. Amer. Math. Soc. 318 (1990) 335 MR956029
8 D A Blanc, Operations on resolutions and the reverse Adams spectral sequence, Trans. Amer. Math. Soc. 342 (1994) 197 MR1132432
9 D Blanc, Algebraic invariants for homotopy types, Math. Proc. Cambridge Philos. Soc. 127 (1999) 497 MR1713125
10 D Blanc, CW simplicial resolutions of spaces with an application to loop spaces, Topology Appl. 100 (2000) 151 MR1733041
11 D Blanc, W G Dwyer, P G Goerss, The realization space of a Π–algebra : a moduli problem in algebraic topology, Topology 43 (2004) 857 MR2061210
12 D Blanc, M W Johnson, J M Turner, On realizing diagrams of Π–algebras, Algebr. Geom. Topol. 6 (2006) 763 MR2240915
13 D Blanc, M W Johnson, J M Turner, Higher homotopy operations and cohomology, J. K-Theory 5 (2010) 167 MR2600286
14 D Blanc, M W Johnson, J M Turner, Higher homotopy operations and André–Quillen cohomology, Adv. Math. 230 (2012) 777 MR2914966
15 D Blanc, M W Johnson, J M Turner, A constructive approach to higher homotopy operations, from: "Homotopy theory: tools and applications" (editors D G Davis, H W Henn, J F Jardine, M W Johnson, C Rezk), Contemp. Math. 729, Amer. Math. Soc. (2019) 21 MR3959595
16 D Blanc, M Markl, Higher homotopy operations, Math. Z. 245 (2003) 1 MR2023950
17 D Blanc, G Peschke, The fiber of functors between categories of algebras, J. Pure Appl. Algebra 207 (2006) 687 MR2265546
18 D Blanc, D Sen, Higher cohomology operations and R–completion, Algebr. Geom. Topol. 18 (2018) 247 MR3748244
19 A K Bousfield, E M Friedlander, Homotopy theory of Γ–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 80 MR513569
20 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
21 W G Dwyer, D M Kan, C R Stover, An E2 model category structure for pointed simplicial spaces, J. Pure Appl. Algebra 90 (1993) 137 MR1250765
22 W G Dwyer, D M Kan, C R Stover, The bigraded homotopy groups πi,jX of a pointed simplicial space X, J. Pure Appl. Algebra 103 (1995) 167 MR1358761
23 E D Farjoun, Cellular spaces, null spaces and homotopy localization, 1622, Springer (1996) MR1392221
24 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
25 B Gray, Homotopy theory: an introduction to algebraic topology, 64, Academic (1975) MR0402714
26 P J Hilton, On the homotopy groups of the union of spheres, J. London Math. Soc. 30 (1955) 154 MR68218
27 P Hilton, G Mislin, J Roitberg, Localization of nilpotent groups and spaces, 15, North-Holland (1975) MR0478146
28 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
29 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
30 J F Jardine, Bousfield’s E2 model theory for simplicial objects, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 305 MR2066504
31 J P May, Simplicial objects in algebraic topology, 11, Van Nostrand (1967) MR0222892
32 R E Mosher, M C Tangora, Cohomology operations and applications in homotopy theory, Harper & Row (1968) MR0226634
33 P Pstrągowski, Moduli of Π–algebras, preprint (2017) arXiv:1705.05761
34 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
35 D Quillen, Rational homotopy theory, Ann. of Math. 90 (1969) 205 MR258031
36 E Spanier, Secondary operations on mappings and cohomology, Ann. of Math. 75 (1962) 260 MR133823
37 E Spanier, Higher order operations, Trans. Amer. Math. Soc. 109 (1963) 509 MR158399
38 N E Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967) 133 MR210075
39 C R Stover, A van Kampen spectral sequence for higher homotopy groups, Topology 29 (1990) 9 MR1046622
40 H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962) MR0143217
41 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
42 G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508