Publications of Douglas C. Ravenel

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ix Publications of Douglas C. Ravenel Books 1. Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, New York, 1986. 2. Nilpotence and periodicity in stable homotopy theory, Annals of Mathematics Studies, Number 128, Princeton, 1992. 3. Complex Cobordism and Stable Homotopy Groups of Spheres, Second Edition, AMS Chelsea Publishing, Providence, 2004, available online at http://www.math.rochester.edu/people/faculty/doug/. Conference proceedings edited 1. Algebraic Topology, Proceedings, Seattle 1985 (with H. R. Miller), Lecture Notes in Mathematics 1286, Springer-Verlag, New York, 1987. 2. Algebraic Topology, Proceedings, Arcata 1986, (with G. Carlsson, R. L. Cohen and H. R. Miller), Lecture Notes in Mathematics 1370, Springer-Verlag, New York, 1989. 3. Homotopy Theory and Its Applications, A Conference on Algebraic Topology in Honor of Samuel Gitler, August 9-13, 1993, Cocoyoc, Mexico (with A. Adem, and R. J. Milgram), Contemporary Mathematics 188, American Mathematical Society, 1995. 4. Elliptic cohomology: Geometry, applications and higher chromatic analogues (with H. R. Miller), London Mathematical Society Lecture Notes Series (no. 342), Cambridge University Press, Cambridge, 2007. Papers 1. A definition of exotic characteristic classes, Comm. Math. Helv., 47 (1972), 421 436. 2. Bipolynomial Hopf algebras (with W. S. Wilson), Journal of Pure and Applied Algebra 4 (1974), 41 45. 3. The Hopf ring for complex cobordism (with W. S. Wilson), Bulletin of the American Mathematical Society, 80 (1974), 1185 1189. 4. Dieudonné modules for Abelian Hopf algebras, Proceeding of the Northwestern University Conference on Homotopy Theory, 1974, Mexican Mathematical Society Monograph, 177 194. 5. Multiplicative operations in BP BP, Pacific Journal of Mathematics, 57 (1975), 539 544 6. Novikov s Ext 2 and the nontriviality of the gamma family (with H. R. Miller and W. S. Wilson), Bulletin of the American Mathematical Society, 81 (1975), 1073 1075. 7. The structure of BP BP modulo an invariant prime ideal, Topology, 15 (1976), 149-154.

x DOUGLAS C. RAVENEL 8. The structure of Morava stabilizer algebras, Inv. Math., 37 (1976), 109 120. 9. The Hopf ring for complex cobordism (with W. S. Wilson), Journal of Pure and Applied Algebra, 8 (1977), 241 280. 10. The cohomology of the Morava stabilizer algebras, Math. Zeit., 152 (1977), 287 297. 11. Morava stabilizer algebras and the localization of Novikov s E 2 -term (with H. R. Miller), Duke Math. J., 44 (1977), 433 447. 12. Periodic phenomena in the Adams-Novikov spectral sequence (with H. R. Miller and W. S. Wilson), Annals of Mathematics, 106 (1977), 469 516. 13. The nonexistence of odd primary Arf invariant elements in stable homotopy, Math. Proc. Camb. Phil. Soc., 83 (1978), 429 443. 14. Complex cobordism and its applications, Proceedings of the International Congress of Mathematicians, Helsinki, 1978, 491 496. 15. A novice s guide to the Adams-Novikov spectral sequence, Geometric Applications of Homotopy Theory, Lecture Notes in Mathematics, Springer Verlag, Vol. 658, 404 475, 1979. 16. Morava K-theories of Eilenberg-MacLane spaces and the Conner-Floyd conjecture (with W. S. Wilson), Amer. J. Math., 102 (1980), 691 748. 17. The Segal conjecture for cyclic groups, Bulletin of the London Mathematical Society, 13 (1981), 42 44. 18. Morava K-theories and finite groups, in Symposium on Algebraic Topology in honor of José Adem (Oaxtepec, 1981), 289 292, Contemporary Mathematics 12, American Mathematical Society, Providence, R.I., 1982. 19. On primitives in BP CP /I n, in Current trends in algebraic topology, Part 1 (London, Ont., 1981), 245 256, CMS Conference Proceedings, 2, American Mathematical Society, Providence, R.I., 1982. 20. The EHP sequence in BP theory (with E. B. Curtis and M. Bendersky), Topology 12 (1982), 373 391. 21. The Segal conjecture for cyclic groups and its consequences, Amer. J. Math., 106 (1984), 414 446. 22. Localization with respect to certain periodic homology theories, Amer. J. Math., 106 (1984), 351 414. 23. Formal A-Modules and the Adams-Novikov spectral sequence, Journal of Pure and Applied Algebra, 32 (1984), 327 345. 24. The Adams-Novikov E 2 -term for a complex with p cells, Amer. J. Math., 107 (1985), 933 968. 25. Spin and statistics of solitons and J-homomorphism (with A. Zee), Communications in Math. Phys., 98 (1985), 239 243. 26. The geometric realization of the chromatic resolution, Algebraic Topology and Algebraic K-theory, pages 168-179, Annals of Math. Studies, Princeton University Press, 1987.

PUBLICATIONS xi 27. Fractal structures in H (BO) and their application to cobordism theory (with V. Giambalvo and D. J. Pengelley), The Lefschetz centennial conference, Part II (Mexico City, 1984), 43 50, Contemporary Mathematics 58, II, American Mathematical Society, Providence, RI, 1987. 28. Toward a global understanding of the homotopy groups of spheres (with M. E. Mahowald), The Lefschetz centennial conference, Part II (Mexico City, 1984), 57 74, Contemporary Mathematics 58, II, American Mathematical Society, Providence, RI, 1987. 29. A fractal algebraic splitting of the classifying space for vector bundles (with V. Giambalvo and D. J. Pengelley), Transactions of the American Mathematical Society 307 (1988), 433 455. 30. Localization and periodicity in stable homotopy theory, Homotopy Theory Proceedings, Durham, 1985, pages 175-194, edited by E. Rees and J. D. S. Jones, Cambridge University Press, Cambridge, 1987. 31. A fractal-like algebraic splitting of the classifying space for vector bundles (with V. Giambalvo and D. J. Pengelley), Transactions of the American Mathematical Society 307 (1988), 433-455. 32. Complex cobordism theory for number theorists, Elliptic Curves and Modular Forms in Algebraic Topology, pages 123 133, Lecture Notes in Mathematics, Vol. 1326, Springer-Verlag, 1988. 33. Homotopy groups of spheres on a small computer, in Computers in Geometry and Topology, pages 259 284, edited by M. C. Tangora, Marcel Dekker, New York, 1989. 34. The nilpotence and periodicity theorems in stable homotopy theory (Séminaire Bourbaki, Exposé 728), Asterisque 189 190 (1990) 399 428. 35. Morava K theories of classifying spaces and generalized characters for finite groups (with M. J. Hopkins and N. Kuhn), in Algebraic Topology: Homotopy, Proceedings, Barcelona 1990, pages 186 209, Lecture Notes in Mathematics, Vol. 1509, Springer-Verlag, 1992. 36. Progress report on the telescope conjecture, in Adams Memorial Symposium on Algebraic Topology:2, pages 1 21, London Math. Soc. Lecture Notes 176, Cambridge University Press, 1992. 37. Suspension spectra are harmonic (with M. J. Hopkins), Bol. Soc. Mat. Mexicana 37 (1992), 217 279. 38. The homology and Morava K theory of Ω 2 SU(n), Forum Mathematicum 5 (1993), 1 21. 39. Mark Mahowald s work in homotopy theory (with H. R. Miller), in Algebraic Topology, Oaxtepec 1991, pages 1 29, Contemporary Mathematics 146, American Mathematical Society, 1993. 40. Life after the telescope conjecture, Algebraic K-theory and Algebraic Topology, pages 215 222, edited by P. G. Goerss and J. F. Jardine, Kluwer Academic Publishers, 1993.

xii DOUGLAS C. RAVENEL 41. Periodic cohomology theories defined by elliptic curves (with P. S. Landweber and R. E. Stong), in The Čech Centennial, pages 317 338, Contemporary Mathematics 181, American Mathematical Society, 1995. 42. The root invariant in homotopy theory (with M. E. Mahowald), Topology 32 (1993), 865 898. 43. Recent developments in stable homotopy theory. XI Latin American School of Mathematics (Spanish) (Mexico City, 1993), 157 235, Aportaciones Mat. Comun., 15, Soc. Mat. Mexicana, Mexxico City, 1995. 44. On the nilpotence order of β 1 (with C.-N. Lee), Math. Proc. Camb. Phil. Soc. 115 (1994), 483 488. 45. Some variations on the telescope conjecture, in The Čech Centennial, pages 391 405, Contemporary Mathematics 181, American Mathematical Society, 1995. 46. The Hopf ring for P (n) (with W. S. Wilson), Canadian Journal of Mathematics 48 (1996), 1044 1063. 47. The 7-connected cobordism ring at p = 3 (with M. A. Hovey), Transactions of the American Mathematical Society 347 (1995), 3473 3502. 48. The stable homotopy theory of finite complexes, Chapter 9 (pages 325 396) of Handbook of Algebraic Topology, edited by I. M. James, Elsevier, 1995. 49. A note on the thick subcategory theorem (with A. Jeanneret and P. S. Landweber), Algebraic Topology: Barcelona Conference on Algebraic Topology, 201 207, Progr. Math., 136, Birkhauser, Basel, 1996. 50. Morava Hopf algebras and spaces K(n)-equivalent to finite Postnikov systems (with M. J. Hopkins and W. S. Wilson), in S. O. Kochman and P. Selick, editors, Stable and Unstable Homotopy, volume 19 of The Fields Institute for Research in Mathematical Sciences Communications Series, pages 137-163, Providence, R.I., 1998. American Mathematical Society. 51. Brown-Peterson cohomology from Morava K-theory (with W. S. Wilson and N. Yagita), K-theory 324:1 52, 1998. 52. A software driven undergraduate fractals course, Fractals, Computer Graphics, and Mathematics Education, edited by M. L. Frame and B. B. Mandelbrot, pages 171 175, Mathematical Association of America, 2002. 53. Bousfield localizations of classifying spaces of nilpotent groups (with E. Dror Farjoun and W. G. Dwyer), Proceedings of the American Mathematical Society 127 (1999), 1855 1861. 54. What we still don t know about loop spaces of spheres, in Homotopy theory via algebraic geometry and group representations, pages 275 292, Contemporary Mathematics 220, American Mathematical Society, 1998. 55. The Thomified Eilenberg-Moore spectral sequence (with M. E. Mahowald and P. Shick), Cohomological Methods in Homotopy Theory, 249 262, Progress in Mathematics 196, Birkhäuser, Basel, 2000. 56. Generalized characters and complex oriented cohomology theories (with M. J. Hopkins and N. Kuhn), Journal of the American Mathematical Society 13 (2000), 553-594.

PUBLICATIONS xiii 57. The triple loop space approach to the telescope conjecture (with M. E. Mahowald and P. Shick), in Homotopy Methods in Algebraic Topology, pages 217 284, Contemporary Mathematics 271, American Mathematical Society, 2001. 58. The microstable Adams-Novikov spectral sequence, Une dégustation topologique [Topological morsels]: homotopy theory in the Swiss Alps (Arolla, 1999), pages 193 209, Contemporary Mathematics 265, American Mathematical Society, Providence, RI, 2000. 59. The method of infinite descent in stable homotopy theory I, Recent Progress in Homotopy Theory, pages 251 284, Contemporary Mathematics 293, American Mathematical Society, 2002. 60. On the generalized Novikov first Ext group modulo a prime (with H. Nakai), Osaka Journal of Mathematics 39 (2002), no. 4, 843 865. 61. The first cohomology group of the generalized Morava stabilizer algebra (with Hiro Nakai), Proceedings of the American Mathematical Society 131 (2003), no. 5, 1629 1639. 62. The chromatic Ext groups Ext 0 Γ(m+1) (BP, M 1 2 ) (with I. Ichigi and H. Nakai)., Transactions of the American Mathematical Society 354 (2002), 3789 3813. 63. Toward higher chromatic analogs of elliptic cohomology, in Elliptic cohomology: Geometry, applications and higher chromatic anlogues (with H. R. Miller), 286 305, London Mathematical Society Lecture Notes Series (no. 342), Cambridge University Press, Cambridge, 2007. 64. The first Adams-Novikov differential for the spectrum T (m), in preparation. 65. Toward higher chromatic analogs of elliptic cohomology II, Homology, Homotopy and Applications 10(3) (2008), 335 368. 66. The method of infinite descent in stable homotopy theory II (with H. Nakai), in preparation. 67. On β-elements in the Adams-Novikov spectral sequence (with H. Nakai), submitted.

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