[Ada:BB] J. F. Adams: Stable homotopy and generalized homology, Chicago Univ. Press 1974

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1 Bibliography [Ada:BB] J. F. Adams: Stable homotopy and generalized homology, Chicago Univ. Press 1974 [AdM71] J. F. Adams, H. R. Margolis: Modules over the Steenrod algebra, Topology 10 (1971), [AnD73] [AnH68] D. W. Anderson, D. W. Davis: A vanishing theorem in homological algebra, Comm. Math. Helv. 48 (1973), D. W. Anderson, L. Hodgkin: The K-theory of Eilenberg-MacLane spaces, Topology 7 (1968), [Ara:TF] S. Araki: Typical formal groups in complex cobordism and K- theory, Lect. in Math. Kyoto Univ., Kinokuniya Book Store Co., Tokyo 1973 [Bar02] Michael Barr. Acyclic models, volume 17 of CRM Monograph Series. American Mathematical Society, Providence, RI, [Boa99] J. Michael Boardman. Conditionally convergent spectral sequences. In Homotopy invariant algebraic structures (Baltimore, MD, 1998), volume 239 of Contemp. Math., pages Amer. Math. Soc., Providence, RI, [BoK72] [Boe84] A. K. Bousfield, D. M. Kan: Homotopy limits, completion and localization, Springer Lecture Notes 304 (1972) C. F. Bödigheimer: Gefärbte Konfigurationen, Dissertation Heidelberg

2 References [Boe87] [Bo79a] C. F. Bödigheimer: Stable splittings of mapping spaces, in Springer Lecture Notes 1286(1987), A. K. Bousfield: The localization of spectra with respect to homology, Topology 18 (1979), [Bo79b] A. K. Bousfield: The Boolean algebra of spectra, Comm. Math. Helv. 54 (1979), , (Correction in 58 (1983), ) [BrC87] E. H. Brown, R. L. Cohen: The Adams spectral sequence of Ω 2 S 3 and Brown-Gitler spectra, Ann. Math. Studies 113 (1987), [CMM78] F. R. Cohen, M. E. Mahowald, R. J. Milgram: The stable decomposition for the double loop space of a sphere, Proc. Symp. Pure Math. 32 (1978) [CLM76] F. R. Cohen, T. Lada, J. P. May: The homology of iterated loop spaces, Springer Lecture Notes 533 (1976) [DHS88] [DP61] [DoT62] [Dwy74] E. S. Devinatz, M. J. Hopkins, J. H. Smith: Nilpotence and stable homotopy theory I, Ann. Math. 128 (1988), Albrecht Dold and Dieter Puppe. Homologie nicht-additiver Funktoren. Anwendungen. Ann. Inst. Fourier Grenoble, 11: , A. Dold, R. Thom: Quasifaserungen und unendliche symmetrische Produkte, Ann. Math. 67 (1958), W. G. Dwyer: Strong convergence of the Eilenberg-Moore spectral sequence, Topology 13 (1974), [DyL62] E. Dyer, R. K. Lashof: Homology of iterated loop spaces, Amer. J. Math. 84 (1962), [EcH66] B. Eckmann, P. Hilton: Exact couples in an abelian category, J. Algebra 3, (1966), [EiM66] S. Eilenberg, J. C. Moore: Homology and fibrations I, Comm. Math. Helv. 40 (1966),

3 2.2. References 91 [GJ99] [Hae71] [Ho84a] Paul G. Goerss and John F. Jardine. Simplicial homotopy theory, volume 174 of Progress in Mathematics. Birkhäuser Verlag, Basel, A. Haefliger: Lectures on the theorem of Gromov, in Proc. Liverpool Singularities-Symp. II, Springer Lecture Notes 209 (1971), M. J. Hopkins: Stable decompositions of certain loop spaces, Dissertation Northwestern Univ [Ho84b] M. J. Hopkins: Some problems in topology, Thesis Oxford Univ [Hop87] [HoP93] [JoY80] [KuA68] [Lew78] M. J. Hopkins: Global methods in homotopy theory, Proc. LMS Symposium on Homotopy Theory, Durham 1985; London Math. Soc. Lect. Note Ser. 117 (1987), M. J. Hopkins, J. H. Palmieri: A nilpotence theorem for modules over the mod 2 Steenrod algebra, Topology 32, No. 4 (1993), D. C. Johnson, Z. Yosimura: Torsion in Brown-Peterson homology and Hurewicz homomorphisms, Osaka J. Math. 17 (1980), T. Kudo, S. Araki: Topology of H n -spaces and H-squaring operations, Mem. Fac. Sci. Kyushu Univ. Ser.A 10 (1956), L. G. Lewis: The stable category and generalized Thom spectra, Dissertation Chicago 1978 [McL:H] S. MacLane: Homology, 3rd ed., Springer 1975 [McD75] D. McDuff: Configuration spaces of positive and negative particles, Topology 14 (1975), [Mah79] M. Mahowald: Ring spectra which are Thom complexes, Duke Math. J. 46 (1979), [Ma:StA] H. R. Margolis: Spectra and the Steenrod algebra, North-Holland Math. Lib. Vol 29., Amsterdam-New York-Oxford (1983)

4 References [Mar74] H. R. Margolis: Eilenberg-Mac Lane spectra, Proc. Amer. math. Soc. 43 (1974), [May72] [Mil81] J. P. May: The geometry of iterated loop spaces, Springer Lecture Notes 271 (1972) H. R. Miller: On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space, J. Pure Appl. Alg. 20 (1981), [MiW81] H. R. Miller, C. Wilkerson: Vanishing lines for modules over the Steenrod algebra, J. Pure Appl. Alg. 22 (1981), [MiM65] J. Milnor, J. C. Moore: On the structure of Hopf algebras, Ann. Math. 81 (1965), [MT:CO] R. E. Mosher, M. C. Tangora: Cohomology operations and applications in homotopy theory, Harper & Row 1968 [MRW77] H. R. Miller, D. C. Ravenel, W. S. Wilson: Periodic phenomena in the Adams-Novikov spectral sequence, Ann. of Math. 106 (1977), [Moo56] [MS68] [Nak57] J. C. Moore: The double suspension and p-primary components of the homotopy groups of spheres, Bol. Soc. Mat. Mex. 1 (1956), J. C. Moore, L. Smith: Hopf algebras and multiplicative fibrations, I., Amer. J. Math. 90 (1968), M. Nakaoka: Cohomology mod p of the p-fold symmetric products of spheres, J. Math. Soc. Japan 9 (1957), [Nis68] G. Nishida: Cohomology operations in iterated loop spaces, Proc. Japan Acad. 44 (1968), [Nis73] [Pal92] G. Nishida: The nilpotence of elements of the stable homotopy groups of spheres, Journ. of the Math. Soc. Japan 25 (1973), J. H. Palmieri: Self-maps of modules over the Steenrod algebra, J. Pure Appl. Alg. 79, No. 3 (1992),

5 2.2. References 93 [Pal94] [PaS94] J. H. Palmieri: The chromatic filtration and the Steenrod algebra, Contemp. Math. 158 (1994), J. H. Palmieri, H. Sadofsky: Self-maps of spectra, a theorem of J. Smith, and Margolis killing construction, Math. Z. 215, No. 3 (1994p), [Rav:CC] D. C. Ravenel: Complex cobordism and stable homotopy groups of spheres, Academic Press 1986 [Rav:NP] D. C. Ravenel: Nilpotence and periodicity in stable homotopy theory, Ann. Math. Studies 128, Princeton University Press 1986 [Rav84] [Rav83] [Rec70] [Smi93] D. C. Ravenel: Localization with respect to certain periodic homology theories, Am. J. Math. 106 (1984), D. C. Ravenel: The geometric realization of the chromatic resolution, Ann. of Math. Stud. 113 (1983), D. L. Rector: Steenrod operations in the Eilenberg-Moore spectral sequence, Comm. Math. Helv. 45 (1970), J. H. Smith: Finite complexes with vanishing lines of small slope Preprint, available at hopf@math. purdue. edu [Smi70] L. Smith: Lectures on the Eilenberg-Moore spectral sequence, Springer Lecture Notes 134 [Sna74] V. P. Snaith: A stable decomposition of Ω n S n X, J. Lond. Math. Soc. 7 (1974), [Spa:AT] E. H. Spanier: Algebraic topology, McGraw-Hill 1966 [StE:CO] N. E. Steenrod, D. B. A. Epstein: Cohomology operations, Ann. of Math. Stud vol. 50, Princeton University Press, Princeton, 1962 [Tsu73] A. Tsuchiya: Homology operations on ring spectrum of H type and their applications, J. Math. Soc. Japan 25 (1973), [Vog70] R. Vogt: Boardman s stable homotopy category, Aarhus Univ. Mat. Inst. Lecture Note Series 21 (1970)

6 References [Vog71] R. Vogt: Convenient categories of topological spaces for homotopy theory, Arch. Math. 22 (1971), [Wil:BP] W. S. Wilson: Brown-Peterson homology: an introduction and sampler, Regional Conf. Series in Math. 48, AMS 1982 [Whi:El] G. W. Whitehead: Elements of homotopy theory, Springer (1978)

Reflection group counting and q-counting

Reflection group counting and q-counting Vic Reiner Univ. of Minnesota reiner@math.umn.edu Summer School on Algebraic and Enumerative Combinatorics S. Miguel de Seide, Portugal July 2-13, 2012 Outline