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Publications of Douglas C. Ravenel

January, 2025

For preprints and slides of recent talks, see my preprints page.

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, available online.
  3. Complex Cobordism and Stable Homotopy Groups of Spheres, Second edition, AMS Chelsea Publishing, Providence, 2004, available online.
  4. Equivariant stable homotopy theory and the Kervaire invariant (with Michael Hill and Michael Hopkins), Cambridge University Press, 2021 available online.

Conference proceedings

  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, 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 A.M.S. , 80 (1974), 1185-1189. 
  4. Dieudonn\'e 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 Ext2 and the nontriviality of the gamma family (with H. R. Miller and W. S. Wilson), Bulletin of the A.M.S. , 81 (1975), 1073-1075. 
  7. The structure of BP_*BP modulo an invariant prime ideal, Topology , 15 (1976), 149-153. 
  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 to homotopy theory, 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, Symposium on Algebraic Topology in honor of José Adem (Oaxtepec, 1981), pp. 289--292, Contemp. Math., 12, Amer. Math. Soc., Providence, R.I., 1982.
  19. On primitives in BP_*CP^\infty/I_n, Current trends in algebraic topology, Part 1 (London, Ont., 1981), pp. 245--256, CMS Conf. Proc., 2, Amer. Math. Soc., 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 E2- 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. 
  27. Fractal structures in H^*(BO) and their application to cobordism theory (with V. Giambalvo and D. J. Pengelley), The Lefschetz Conference Proceeding in Algebraic Topology, pages 43-50, Contemporary Mathematics , Vol. 1958, American Mathematical Society, 1987. 
  28. Toward a global understanding of the homotopy groups of spheres (with M. E. Mahowald), The Lefschetz Conference Proceeding in Algebraic Topology , pages 57-74, Contemporary Mathematics 58, American Mathematical Society, 1987. 
  29. A fractal algebraic splitting of the classifying space for vector bundles (with V. Giambalvo and D. J. Pengelley), Transactions of the Amer. Math. Soc. 307(1988), 433--455.
  30. Localization and periodicity in 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. 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. 
  32. 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. 
  33. The nilpotence and periodicity theorems in stable homotopy theory (S\'eminaire Bourbaki, Expos\'e 728), Asterisque 189-190(1990) 399-428. 
  34. Morava K-theories of classifying spaces and generalized characters for finite groups (with M. J. Hopkins and N. Kuhn), in Algebraic topology (San Feliu de Guíxols,1990), 186--209, Lecture Notes in Math., 1509, Springer, Berlin, 1992. 
  35. 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.
  36. Suspension spectra are harmonic (with M. J. Hopkins), Bol. Soc. Mat. Mexicana , 37(1992), 217-279. 
  37. The homology and Morava K-theory of Ω2SU(n), Forum Mathematicum , 5(1993), 1-21. 
  38. 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.
  39. Life after the telescope conjecture , Algebraic K-theory and Algebraic Topology , pages 215-222, edited by P. G. Goerss and R. F. Jardine, Kluwer Academic Publishers, 1993. 
  40. Periodic cohomology theories defined by elliptic curves (with P. S. Landweber and R. E. Stong), in The Cech Centennial: A Conference on Homotopy Theory (edited by M. Cenkl and H. R. Miller), pages 317-338, Contemporary Mathematics 181, American Mathematical Society, 1995. 
  41. The root invariant in homotopy theory (with M. E. Mahowald), Topology 32(1993), 865-898.
  42. Recent developments in stable homotopy theory. XI Latin American Schoolof Mathematics (Spanish) (Mexico City, 1993), 157--235, Aportaciones Mat. Comun., 15, Soc. Mat. Mexicana,México City, 1995.
  43. On the nilpotence order of β1 (with C.-N. Lee), Math. Proc. Camb. Phil. Soc. 115(1994), 483-488. 
  44. Some variations on the telescope conjecture , in The Cech Centennial: A Conference on Homotopy Theory (edited by M. Cenkl and H. R. Miller), pages 391-405, Contemporary Mathematics 181, American Mathematical Society, 1995. 
  45. The Hopf ring for P(n) (with W. S. Wilson), Canadian Journal of Mathematics 48 (1996), 1044-1063. 
  46. The 7-connected cobordism ring at p=3 (with M. A. Hovey), Transactions of the Amer. Math. Soc. , 347(1995), 3473-3502. Preprint.
  47. The stable homotopy theory of finite complexes, Chapter 9 (pages 325--396) of Handbook of Algebraic Topology , edited by I. M. James, Elsevier, 1995. 
  48. 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. 
  49. 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.
  50. Brown-Peterson cohomology from Morava K-theory (with W. S. Wilson and N. Yagita), K-theory , 15:149-200, 1998.
  51. 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.
  52. Bousfield localizations of classifying spaces of nilpotent groups (with E. Dror Farjoun and W. G. Dwyer), Proceedings of the Amer. Math. Soc. 127(1999), 1855-1861.
  53. What we still don't know about loop spaces of spheres , in Homotopy theory via algebraic geometry and group representations (edited by Mark Mahowald and Stewart Priddy), pages 275-292, Contemporary Mathematics 220, American Mathematical Society, 1998.
  54. The Thomified Eilenberg-Moore spectral sequence (with M. E. Mahowald and P. Shick),  Cohomological Methods in Homotopy Theory , 249-262, Progr. Math., 196, Birkhauser , Basel, 2000.
  55. Generalized characters and complex oriented cohomology theories (with M. J. Hopkins and N. Kuhn), Journal of the A. M. S. 13 (2000), 553-594.
  56. The triple loop space approach to the telescope conjecture (with M. E. Mahowald and P. Shick), in Homotopy Methods in Algebraic Topology, Contemp. Math.  271, pp 217-284, AMS, 2001.
  57. The microstable Adams-Novikov spectral sequence , Une dégustation topologique [Topological morsels]: homotopy theory in the Swiss Alps (Arolla, 1999), 193--209, Contemp. Math., 265 , Amer. Math. Soc., Providence, RI, 2000.
  58. The method of infinite descent in stable homotopy theory I , in Recent Progress in Homotopy Theory,   Contemp. Math.  293,  251-284, AMS, 2002.
  59. On the generalized Novikov first Ext group modulo a prime (with H. Nakai), Osaka Journal of Mathematics 39  (2002),  no. 4, 843-865.
  60. The first cohomology group of the generalized Morava stabilizer algebra (with H. Nakai),  Proc. Amer. Math. Soc.  131 (2003), no. 5, 1629--1639
  61. The chromatic Ext groups $\Ext_{\Gamma(m+1)}^{0}(BP_{*},M_2^{1})$  (with  I. Ichigi and H. Nakai),  Trans. Amer. Math. Soc. 354 (2002), 3789-3813.
  62. Toward higher chromatic analogs of elliptic cohomology, in Elliptic Cohomology Geometry, Applications, and Higher Chromatic Analogues, London Mathematical Society Lecture Notes Series (No. 342), Cambridge University Press, 2007.
  63. The first Adams-Novikov differential for the spectrum T (m) , in preparation.
  64. Toward higher chromatic analogs of elliptic cohomology II, Homology, Homotopy and Applications, vol. 10(3), 2008, pp.335--368.
  65. On β-elements in the Adams-Novikov spectral sequence (with H. Nakai), Journal of Topology, 2009, 2: 295-320.
  66. The Arf-Kervaire problem in algebraic topology: an introduction (with M. Hill and M. Hopkins), Current Developments in Mathematics, 2009, International Press, 2010, pages 23-57.
  67. The Kervaire invariant one problem in algebraic topology: proof (with M. Hill and M. Hopkins), written for Current Developments in Mathematics, 2010, International Press, 2011, pages 1-43.
  68. A solution to the Arf-Kervaire problem (with M. Hill and M. Hopkins), Proceedings of Gokova Geometry-Topology Conference 2010, pages 21-63.
  69. Quillen's work on formal group laws and complex cobordism theory, Journal of K-Theory 11 (2013), no. 3, 493-506.
  70. On the non-existence of elements of Kervaire invariant one (with M. Hill and M. Hopkins), Annals of Mathematics 184 (2016), 1-262.
  71. The slice spectral sequence of Mackey functors for the C4-analog of real K-theory (with M. Hill and M. Hopkins), Forum Math. 2017; 29 (2):383-447. This paper has typos (pointed out by Agnes Beaudry and Mingcong Zeng) in the spectral sequence chart of Figure 16, namely a missing d11, d7 and d13 originating in dimensions 32, 36 and 37. The corrected chart is here.
  72. The slice spectral sequence for certain RO(C p n)-graded suspensions of HZ (with M. Hill and M. Hopkins), Boletin de la Sociedad Matematica Mexicana 2017; 23 (1):289-317.
  73. On the 3-primary Arf-Kervaire invariant problem (with M. Hill and M. Hopkins), in preparation.
  74. Remembering Mark Mahowald 1931-2013. Notices of Amer. Math. Soc. 63 (2016), 652-656. Unabridged version.
  75. The cohomology of C2-equivariant A(1) and the homotopy of koC2 (with B. J. Guillou, M. Hill and D. C. Isaksen), Tunisian Journal of Mathematics, 3 (2020), 567-632.
  76. The connective Morava K-theory of the second mod p Eilenberg-MacLane space (with D. M. Davis and W. S. Wilson), to appear.
  77. What is an infinity-category? Graduate Journal of Mathematics, Volume 8, Issue 2 (2023).
  78. The homological slice spectral sequence in motivic and real bordism (with Christian Carrick and Michael A. Hill), Advances in Mathematics 458 (2024), Paper No. 109955, 74 pp.
  79. The method of infinite descent in stable homotopy theory II (with H. Nakai), New York J. Math. 30 (2024), 231-269.

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