Algebraic & Geometric Topology Volume 10, issue 1 (2010)

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Homotopy nilpotent groups

Georg Biedermann and William G Dwyer

Algebraic & Geometric Topology 10 (2010) 33–61

DOI: 10.2140/agt.2010.10.33

Bibliography

1	G Arone, M Ching, Operads and chain rules for the calculus of functors arXiv:0902.0399
2	G Arone, W G Dwyer, K Lesh, Loop structures in Taylor towers, Algebr. Geom. Topol. 8 (2008) 173 MR2377281
3	G Arone, M Kankaanrinta, A functorial model for iterated Snaith splitting with applications to calculus of functors, from: "Stable and unstable homotopy (Toronto, ON, 1996)" (editors W G Dwyer, S Halperin, R Kane, S O Kochman, M E Mahowald, P S Selick), Fields Inst. Commun. 19, Amer. Math. Soc. (1998) 1 MR1622334
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	B Badzioch, Algebraic theories in homotopy theory, Ann. of Math. $(2)$ 155 (2002) 895 MR1923968
6	B Badzioch, K Chung, A A Voronov, The canonical delooping machine, J. Pure Appl. Algebra 208 (2007) 531 MR2277692
7	G Biedermann, B Chorny, O Röndigs, Calculus of functors and model categories, Adv. Math. 214 (2007) 92 MR2348024
8	G Biedermann, W G Dwyer, Homotopy nilpotent spaces, work in progress
9	A K Bousfield, E M Friedlander, Homotopy theory of $\Gamma $–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II", Lecture Notes in Math. 658, Springer (1978) 80 MR513569
10	M Ching, A chain rule for Goodwillie derivatives of functors from spectra to spectra, to appear in Trans. Amer. Math. Soc. arXiv:math.AT/07105567
11	M Ching, Bar constructions for topological operads and the Goodwillie derivatives of the identity, Geom. Topol. 9 (2005) 833 MR2140994
12	E B Curtis, Some relations between homotopy and homology, Ann. of Math. $(2)$ 82 (1965) 386 MR0184231
13	A Dold, Homology of symmetric products and other functors of complexes, Ann. of Math. $(2)$ 68 (1958) 54 MR0097057
14	W G Dwyer, Localizations, from: "Axiomatic, enriched and motivic homotopy theory" (editor J P C Greenlees), NATO Sci. Ser. II Math. Phys. Chem. 131, Kluwer Acad. Publ. (2004) 3 MR2061850
15	W G Dwyer, D M Kan, Homotopy theory and simplicial groupoids, Nederl. Akad. Wetensch. Indag. Math. 46 (1984) 379 MR770723
16	W G Dwyer, D M Kan, Equivalences between homotopy theories of diagrams, from: "Algebraic topology and algebraic $K$–theory (Princeton, N.J., 1983)" (editor W Browder), Ann. of Math. Stud. 113, Princeton Univ. Press (1987) 180 MR921478
17	G Ellis, R Steiner, Higher-dimensional crossed modules and the homotopy groups of $(n+1)$–ads, J. Pure Appl. Algebra 46 (1987) 117 MR897011
18	P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Math. 174, Birkhäuser Verlag (1999) MR1711612
19	T G Goodwillie, Calculus. II. Analytic functors, $K$–Theory 5 (1992) 295 MR1162445
20	T G Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003) 645 MR2026544
21	M Hall Jr., A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950) 575 MR0038336
22	P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003) MR1944041
23	J F Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987) 35 MR906403
24	B Johnson, The derivatives of homotopy theory, Trans. Amer. Math. Soc. 347 (1995) 1295 MR1297532
25	A Joyal, Letter to A Grothendieck
26	N J Kuhn, Goodwillie towers and chromatic homotopy: an overview, from: "Proceedings of the Nishida Fest (Kinosaki 2003)" (editors M Ando, N Minami, J Morava, W S Wilson), Geom. Topol. Monogr. 10 (2007) 245 MR2402789
27	F W Lawvere, Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963) 869 MR0158921
28	A Mauer-Oats, Goodwillie calculi, PhD thesis, University of Illinois Urbana-Champaign (2002)
29	A Mauer-Oats, Algebraic Goodwillie calculus and a cotriple model for the remainder, Trans. Amer. Math. Soc. 358 (2006) 1869 MR2197433
30	C Reedy, Homology of algebraic theories, PhD thesis, University of California, San Diego (1974)
31	S Schwede, Stable homotopy of algebraic theories, Topology 40 (2001) 1 MR1791267
32	J P Serre, Lie algebras and Lie groups, Lecture Notes in Math. 1500, Springer (1992) MR1176100
33	E H Spanier, Algebraic topology, McGraw-Hill (1966) MR0210112