Algebraic & Geometric Topology Volume 20, issue 6 (2020)

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$\mathcal{E}_n$–Hopf invariants

Felix Wierstra

Algebraic & Geometric Topology 20 (2020) 2905–2956

DOI: 10.2140/agt.2020.20.2905

Bibliography

1	J F Adams, On the cobar construction, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 409 MR79266
2	J F Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960) 20 MR141119
3	C Berger, Un groupoïde simplicial comme modèle de l’espace des chemins, Bull. Soc. Math. France 123 (1995) 1 MR1330785
4	C Berger, B Fresse, Combinatorial operad actions on cochains, Math. Proc. Cambridge Philos. Soc. 137 (2004) 135 MR2075046
5	J M Boardman, B Steer, On Hopf invariants, Comment. Math. Helv. 42 (1967) 180 MR221503
6	E B Curtis, Simplicial homotopy theory, Adv. Math. 6 (1971) 107 MR279808
7	G C Drummond-Cole, J Hirsh, Model structures for coalgebras, Proc. Amer. Math. Soc. 144 (2016) 1467 MR3451225
8	W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
9	M Filakovsky, P Franek, U Wanger, S Zhechev, Computing simplicial representatives of homotopy group elements, from: "Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms" (editor A Czumaj), SIAM (2018) 1135 MR3775862
10	B Fresse, On the homotopy of simplicial algebras over an operad, Trans. Amer. Math. Soc. 352 (2000) 4113 MR1665330
11	B Fresse, Koszul duality of operads and homology of partition posets, 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) 115 MR2066499
12	B Fresse, Operadic cobar constructions, cylinder objects and homotopy morphisms of algebras over operads, from: "Alpine perspectives on algebraic topology" (editors C Ausoni, K Hess, J Scherer), Contemp. Math. 504, Amer. Math. Soc. (2009) 125 MR2581912
13	B Fresse, The bar complex of an E–infinity algebra, Adv. Math. 223 (2010) 2049 MR2601008
14	B Fresse, Iterated bar complexes of E–infinity algebras and homology theories, Algebr. Geom. Topol. 11 (2011) 747 MR2782544
15	B Fresse, Koszul duality of E_n–operads, Selecta Math. 17 (2011) 363 MR2803847
16	B Fresse, On mapping spaces of differential graded operads with the commutative operad as target, Math. Res. Lett. 18 (2011) 215 MR2784668
17	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
18	P Hu, Higher string topology on general spaces, Proc. Lond. Math. Soc. 93 (2006) 515 MR2251161
19	J L Loday, B Vallette, Algebraic operads, 346, Springer (2012) MR2954392
20	S Mac Lane, Homology, 114, Springer (1963) MR0156879
21	J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
22	J E McClure, J H Smith, Multivariable cochain operations and little n–cubes, J. Amer. Math. Soc. 16 (2003) 681 MR1969208
23	J Millès, The Koszul complex is the cotangent complex, Int. Math. Res. Not. 2012 (2012) 607 MR2885984
24	D Robert-Nicoud, F Wierstra, Homotopy morphisms between convolution homotopy Lie algebras, J. Noncommut. Geom. 13 (2019) 1463 MR4059826
25	D Sinha, B Walter, Lie coalgebras and rational homotopy theory, II : Hopf invariants, Trans. Amer. Math. Soc. 365 (2013) 861 MR2995376
26	N E Steenrod, Cohomology invariants of mappings, Ann. of Math. 50 (1949) 954 MR31231
27	B Vallette, Homotopy theory of homotopy algebras, Ann. Inst. Fourier (Grenoble) 70 (2020) 683 MR4105949
28	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
29	G W Whitehead, A generalization of the Hopf invariant, Ann. of Math. 51 (1950) 192 MR41435
30	G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508