Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Operations on spectral partition Lie algebras and TAQ cohomology

Adela YiYu Zhang

Geometry & Topology 29 (2025) 4477–4529
DOI: 10.2140/gt.2025.29.4477
Bibliography
1 O Antolín Camarena, The mod2 homology of free spectral Lie algebras, Trans. Amer. Math. Soc. 373 (2020) 6301 MR4155178
2 G Arone, A note on the homology of Σn, the Schwartz genus, and solving polynomial equations, from: "An alpine anthology of homotopy theory" (editors D Arlettaz, K Hess), Contemp. Math. 399, Amer. Math. Soc. (2006) 1 MR2222501
3 G Z Arone, D L B Brantner, The action of Young subgroups on the partition complex, Publ. Math. Inst. Hautes Études Sci. 133 (2021) 47 MR4292739
4 G Arone, M Mahowald, The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres, Invent. Math. 135 (1999) 743 MR1669268
5 G Z Arone, W G Dwyer, K Lesh, Bredon homology of partition complexes, Doc. Math. 21 (2016) 1227 MR3578208
6 M Basterra, André–Quillen cohomology of commutative S-algebras, J. Pure Appl. Algebra 144 (1999) 111 MR1732625
7 M Behrens, C Rezk, The Bousfield–Kuhn functor and topological André–Quillen cohomology, Invent. Math. 220 (2020) 949 MR4094969
8 J M Boardman, Conditionally convergent spectral sequences, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 49 MR1718076
9 A K Bousfield, Operations on derived functors of non-additive functors, preprint (1967)
10 A K Bousfield, E B Curtis, A spectral sequence for the homotopy of nice spaces, Trans. Amer. Math. Soc. 151 (1970) 457 MR267586
11 D L B Brantner, The Lubin–Tate theory of spectral Lie algebras, PhD thesis, Harvard University (2017) MR4172386
12 L Brantner, A Mathew, Deformation theory and partition Lie algebras, preprint (2019) arXiv:1904.07352
13 L Brantner, R Campos, J Nuiten, PD operads and explicit partition Lie algebras, preprint (2021) arXiv:2104.03870
14 D L B Brantner, J Hahn, B Knudsen, The Lubin–Tate theory of configuration spaces, I, J. Topol. 17 (2024) MR4822928
15 R R Bruner, J P May, J E McClure, M Steinberger, H ring spectra and their applications, 1176, Springer (1986) MR836132
16 R M Bryant, L G Kovács, R Stöhr, Subalgebras of free restricted Lie algebras, Bull. Austral. Math. Soc. 72 (2005) 147 MR2162300
17 H Cartan, J P Serre, Séminaire Henri Cartan : Algèbres d’Eilenberg–MacLane et homotopie, 1954/55, École Normale Supérieure. Paris : Secrétariat mathématique. 234 p. (Hektograph.) (1955). Erratum Général. ibid., 13 p. (1956)., Secrétariat mathématique, École Normale Supérieure (1955)
18 M Ching, Bar constructions for topological operads and the Goodwillie derivatives of the identity, Geom. Topol. 9 (2005) 833 MR2140994
19 M Ching, J E Harper, Derived Koszul duality and TQ-homology completion of structured ring spectra, Adv. Math. 341 (2019) 118 MR3872846
20 F R Cohen, T J Lada, J P May, The homology of iterated loop spaces, 533, Springer (1976) MR436146
21 V Drinfeld, A letter from Kharkov to Moscow, EMS Surv. Math. Sci. 1 (2014) 241 MR3285856
22 W G Dwyer, Homotopy operations for simplicial commutative algebras, Trans. Amer. Math. Soc. 260 (1980) 421 MR574789
23 E Dyer, R K Lashof, Homology of iterated loop spaces, Amer. J. Math. 84 (1962) 35 MR141112
24 J Francis, D Gaitsgory, Chiral Koszul duality, Selecta Math. 18 (2012) 27 MR2891861
25 B Fresse, On the homotopy of simplicial algebras over an operad, Trans. Amer. Math. Soc. 352 (2000) 4113 MR1665330
26 V Ginzburg, M Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203 MR1301191
27 P G Goerss, On the André–Quillen cohomology of commutative F2-algebras, 186, Soc. Math. France (1990) 169 MR1089001
28 N Jacobson, Restricted Lie algebras of characteristic p, Trans. Amer. Math. Soc. 50 (1941) 15 MR5118
29 B Johnson, The derivatives of homotopy theory, Trans. Amer. Math. Soc. 347 (1995) 1295 MR1297532
30 N Johnson, J Noel, Lifting homotopy T-algebra maps to strict maps, Adv. Math. 264 (2014) 593 MR3250294
31 J J Kjaer, On the odd primary homology of free algebras over the spectral lie operad, J. Homotopy Relat. Struct. 13 (2018) 581 MR3856302
32 N Konovalov, Algebraic Goodwillie spectral sequence, preprint (2023) arXiv:2303.06240
33 D Kraines, T Lada, The cohomology of the Dyer–Lashof algebra, from: "Proceedings of the Northwestern Homotopy Theory Conference" (editors H R Miller, S B Priddy), Contemp. Math. 19, Amer. Math. Soc. (1983) 145 MR711048
34 I Kriz, Towers of E ring spectra with an application to BP, preprint (1993)
35 T Kudo, S Araki, Topology of Hn-spaces and H-squaring operations, Mem. Fac. Sci. Kyūsyū Univ. A 10 (1956) 85 MR87948
36 N J Kuhn, New relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 185 MR1851255
37 T Lawson, En-spectra and Dyer–Lashof operations, from: "Handbook of homotopy theory" (editor H Miller), CRC (2020) 793 MR4197999
38 J Lurie, Derived algebraic geometry, X: Formal moduli problems, preprint (2011)
39 J Lurie, Higher algebra, preprint (2017)
40 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR420610
41 J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
42 H R Miller, Nishida relations and Singer construction, preprint (2014)
43 M Nakaoka, Cohomology mod p of the p-fold symmetric products of spheres, J. Math. Soc. Japan 9 (1957) 417 MR121787
44 M Nakaoka, Cohomology mod p of symmetric products of spheres, J. Inst. Polytech. Osaka City Univ. Ser. A 9 (1958) 1 MR121788
45 G Nishida, Cohomology operations in iterated loop spaces, Proc. Japan Acad. 44 (1968) 104 MR240811
46 S B Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970) 39 MR265437
47 S Priddy, Modp right derived functor algebras of the symmetric algebra functor, J. Pure Appl. Algebra 3 (1973) 337 MR342592
48 J P Pridham, Unifying derived deformation theories, Adv. Math. 224 (2010) 772 MR2628795
49 C Rezk, Rings of power operations for Morava E-theories are Koszul, preprint (2012) arXiv:1204.4831
50 P Salvatore, Configuration operads, minimal models and rational curves, PhD thesis, University of Oxford (1998)
51 S i Takayasu, On stable summands of Thom spectra of B(Z∕2)n associated to Steinberg modules, J. Math. Kyoto Univ. 39 (1999) 377 MR1709300
52 A Y Zhang, Quillen homology of spectral Lie algebras with application to mod p homology of labeled configuration spaces, Algebr. Geom. Topol. 25 (2025) 1945 MR4950893