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Publications of Douglas C. Ravenel
February, 2024
For preprints and slides of recent talks, see
my preprints page.
Books
 Complex
Cobordism and Stable Homotopy Groups of Spheres, Academic Press, New York, 1986.
 Nilpotence
and Periodicity in Stable Homotopy Theory , Annals of
Mathematics Studies, Number 128, Princeton, 1992, available
online .
 Complex
Cobordism and Stable Homotopy Groups of Spheres, Second
edition, AMS Chelsea Publishing, Providence, 2004, available
online .
 Equivariant stable homotopy theory and the Kervaire invariant
(with Michael Hill and Michael Hopkins), Cambridge University Press, 2021 available
online .
Conference proceedings
 Algebraic Topology, Proceedings, Seattle 1985 (with H. R.
Miller),
Lecture Notes in Mathematics 1286, SpringerVerlag, New York, 1987.
 Algebraic Topology, Proceedings, Arcata 1986, (with G.
Carlsson, R. L. Cohen and H. R. Miller),
Lecture Notes in Mathematics 1370, SpringerVerlag, New York, 1989.
 Homotopy Theory and Its Applications, A Conference on
Algebraic Topology in Honor of Samuel Gitler August 913, 1993,
Cocoyoc, Mexico (with A. Adem, and R. J. Milgram),
Contemporary Mathematics 188, American Mathematical Society, 1995.
 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
 A definition of exotic characteristic classes,
Comm. Math. Helv. , 47 (1972), 421436.
 Bipolynomial Hopf algebras (with W. S. Wilson),
Journal of Pure and Applied Algebra 4 (1974),
4145.
 The Hopf ring for complex
cobordism (with W. S. Wilson), Bulletin of the A.M.S. ,
80 (1974), 11851189.
 Dieudonn\'e modules for Abelian Hopf algebras, Proceeding of the
Northwestern University Conference on Homotopy Theory, 1974, Mexican
Mathematical Society Monograph, 177194.
 Multiplicative
operations in BP^{*}BP, Pacific Journal of
Mathematics , 57 (1975), 539544
 Novikov's
Ext^{2} and the nontriviality of the gamma family
(with H. R. Miller and W. S. Wilson), Bulletin of the A.M.S. ,
81 (1975), 10731075.
 The structure of
BP_*BP modulo an invariant prime ideal,
Topology , 15 (1976), 149153.
 The structure of Morava
stabilizer algebras,
Inv. Math. , 37 (1976), 109120.
 The Hopf ring for
complex cobordism (with W. S. Wilson),
Journal of Pure and Applied Algebra , 8 (1977),
241280.
 The cohomology of the Morava
stabilizer algebras,
Math. Zeit. , 152 (1977), 287297.
 Morava stabilizer algebras and the
localization of Novikov's E_2 term (with H. R. Miller),
Duke
Math. J. , 44(1977), 433447.
 Periodic phenomena in the AdamsNovikov spectral sequence (with
H. R. Miller and W. S. Wilson), Annals
of Mathematics , 106 (1977), 469516.
 The nonexistence of odd primary Arf invariant
elements in stable homotopy, Math.
Proc. Camb. Phil. Soc. , 83 (1978),
429443.
 Complex cobordism and its applications to homotopy
theory, Proceedings of the International Congress of
Mathematicians, Helsinki, 1978, 491496.
 A novice's guide to the AdamsNovikov spectral sequence,
Geometric Applications of Homotopy Theory,
Lecture Notes in Mathematics , SpringerVerlag, Vol. 658,
404475, 1979.
 Morava Ktheories of
EilenbergMacLane spaces and the ConnerFloyd conjecture (with
W. S. Wilson),
Amer. J. Math. , 102 (1980), 691748.
 The Segal conjecture for cyclic
groups,
Bulletin of the London Mathematical Society , 13
(1981), 4244.

Morava K theories and finite groups, Symposium on
Algebraic Topology in honor of José Adem (Oaxtepec, 1981),
pp. 289292,
Contemp. Math., 12, Amer. Math. Soc., Providence, R.I.,
1982.
 On primitives in BP_*CP^\infty/I_n, Current trends
in algebraic topology, Part 1 (London, Ont., 1981), pp. 245256,
CMS Conf. Proc., 2, Amer. Math. Soc., Providence, R.I.,
1982.
 The EHP sequence in BP theory (with E. B. Curtis and M.
Bendersky), Topology
12 (1982), 373391.
 The Segal conjecture for cyclic
groups and its consequences,
Amer. J. Math. , 106 (1984), 414446.
 Localization with respect to certain
periodic homology theories,
Amer. J. Math. , 106 (1984), 351414.
 Formal AModules and the
AdamsNovikov spectral sequence,
Journal of Pure and Applied Algebra , 32 (1984),
327345.
 The AdamsNovikov
E_{2} term for a complex with p cells,
Amer. J. Math. , 107 (1985), 933968.
 Spin and statistics of solitons and Jhomomorphism (with
A. Zee),
Communications in Math. Phys. , 98 (1985), 239243.
 The geometric realization of the chromatic resolution, Algebraic
Topology and Algebraic Ktheory, pages 168179, Annals of
Math.
Studies , Princeton University Press, 1987.
 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 4350,
Contemporary Mathematics , Vol. 1958, American Mathematical
Society, 1987.
 Toward
a global understanding of the homotopy groups of spheres (with M.
E. Mahowald), The Lefschetz Conference Proceeding in Algebraic
Topology , pages 5774,
Contemporary Mathematics 58, American Mathematical Society,
1987.
 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), 433455.
 Localization and periodicity in homotopy theory, Homotopy
Theory Proceedings, Durham, 1985, pages 175194, edited by E. Rees
and J. D. S. Jones, Cambridge
University
Press , Cambridge, 1987.
 Complex cobordism theory
for number theorists , Elliptic Curves and Modular Forms in
Algebraic Topology, pages 123133,
Lecture Notes in Mathematics , Vol. 1326, SpringerVerlag,
1988.
 Homotopy groups of spheres on a small computer, in Computers
in Geometry and Topology, pages 259284, edited by M. C. Tangora, Marcel Dekker, New York,
1989.
 The nilpotence and periodicity
theorems in stable homotopy theory (S\'eminaire Bourbaki, Expos\'e
728),
Asterisque 189190(1990) 399428.
 Morava Ktheories of classifying spaces and
generalized characters for finite groups (with M. J. Hopkins and N.
Kuhn), in Algebraic topology (San Feliu de Guíxols,1990),
186209,
Lecture Notes in Math., 1509, Springer, Berlin, 1992.
 Progress report on the
telescope conjecture , in Adams
Memorial Symposium on Algebraic Topology:2 , pages 121,
London Math. Soc. Lecture Notes 176, Cambridge University Press,
1992.
 Suspension spectra are harmonic (with M.
J. Hopkins),
Bol. Soc. Mat. Mexicana , 37(1992), 217279.

The homology and Morava Ktheory of Ω^{2}SU(n),
Forum Mathematicum
, 5(1993), 121.
 Mark Mahowald's work in homotopy
theory (with H. R. Miller), in Algebraic Topology, Oaxtepec
1991, pages 129,
Contemporary Mathematics 146, American Mathematical Society, 1993.
 Life after the telescope conjecture ,
Algebraic Ktheory and Algebraic Topology , pages 215222,
edited by P. G. Goerss and R. F. Jardine, Kluwer Academic Publishers,
1993.
 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 317338,
Contemporary Mathematics 181, American Mathematical Society,
1995.
 The root invariant in homotopy theory
(with M. E. Mahowald),
Topology 32(1993), 865898.
 Recent developments in stable homotopy theory. XI Latin
American Schoolof Mathematics (Spanish) (Mexico City, 1993),
157235, Aportaciones Mat. Comun., 15, Soc. Mat.
Mexicana,México City, 1995.
 On the nilpotence order of
β_{1}
(with C.N. Lee), Math.
Proc. Camb. Phil. Soc. 115(1994), 483488.
 Some variations on the telescope conjecture
, in
The Cech Centennial: A Conference on Homotopy Theory
(edited by M. Cenkl and H. R. Miller), pages 391405,
Contemporary Mathematics 181, American Mathematical Society,
1995.
 The Hopf ring for P(n) (with W. S. Wilson),
Canadian Journal
of Mathematics 48 (1996), 10441063.
 The 7connected cobordism ring at p=3
(with M. A. Hovey),
Transactions of the Amer. Math. Soc. , 347(1995),
34733502. Preprint.
 The stable homotopy theory of finite complexes, Chapter 9 (pages
325396) of
Handbook of Algebraic Topology , edited by I. M. James,
Elsevier, 1995.
 A note on the thick subcategory theorem
(with A. Jeanneret and P. S. Landweber), Algebraic
Topology: Barcelona Conference on Algebraic Topology ,
201207, Progr. Math., 136,
Birkhauser , Basel, 1996.
 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 137163,
Providence, R.I.,
1998. American Mathematical Society.
 BrownPeterson cohomology from Morava Ktheory
(with W. S. Wilson and N. Yagita),
Ktheory , 15:149200, 1998.
 A software driven undergraduate fractals
course, Fractals, Computer Graphics, and
Mathematics Education , edited by M. L. Frame and B. B.
Mandelbrot, pages 171175. Mathematical Association of America,
2002.
 Bousfield localizations of classifying
spaces of nilpotent groups (with E. Dror Farjoun and W. G. Dwyer), Proceedings of the Amer. Math. Soc.
127(1999), 18551861.
 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 275292,
Contemporary Mathematics 220, American Mathematical Society,
1998.
 The Thomified EilenbergMoore spectral
sequence (with M. E. Mahowald and P. Shick),
Cohomological Methods in Homotopy Theory , 249262, Progr.
Math., 196, Birkhauser , Basel,
2000.
 Generalized characters and complex oriented
cohomology theories (with M. J. Hopkins and N. Kuhn), Journal
of the A. M. S. 13 (2000), 553594.
 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 217284, AMS, 2001.
 The microstable
AdamsNovikov spectral sequence , Une dégustation
topologique [Topological morsels]: homotopy theory in the Swiss Alps
(Arolla, 1999), 193209,
Contemp. Math., 265 , Amer. Math. Soc., Providence, RI,
2000.
 The method of infinite descent in stable
homotopy theory I , in Recent Progress in Homotopy Theory,
Contemp. Math. 293, 251284, AMS, 2002.
 On the
generalized Novikov first Ext group modulo a prime (with H. Nakai),
Osaka Journal of Mathematics 39 (2002), no. 4,
843865.
 The first cohomology group of the generalized
Morava stabilizer algebra (with H. Nakai), Proc. Amer. Math. Soc. 131
(2003), no. 5, 16291639
 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), 37893813.
 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.
 The first AdamsNovikov
differential for the spectrum T (m) , in preparation.
 Toward higher
chromatic analogs of elliptic cohomology
II, Homology, Homotopy
and Applications, vol. 10(3), 2008, pp.335368.
 The method of infinite
descent in stable homotopy theory II (with H. Nakai) , in
preparation.
 On βelements in the
AdamsNovikov spectral sequence (with
H. Nakai), Journal
of Topology, 2009, 2: 295320.
 The ArfKervaire
problem in algebraic topology: an introduction (with M. Hill and
M. Hopkins), Current Developments in Mathematics,
2009, International Press, 2010, pages 2357.
 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 143.
 A solution to the
ArfKervaire problem (with M. Hill and
M. Hopkins), Proceedings
of Gokova GeometryTopology Conference 2010, pages 2163.
 Quillen's work
on formal group laws and complex cobordism theory, Journal of
KTheory 11 (2013), no. 3, 493506.
 On the
nonexistence of elements of Kervaire invariant one (with
M. Hill and M. Hopkins), Annals of
Mathematics 184 (2016), 1262.
 The slice spectral sequence
of Mackey functors for the C_{4}analog of
real Ktheory (with M. Hill and M. Hopkins), Forum
Math. 2017; 29 (2):383447. This paper has typos (pointed out by
Agnes Beaudry and Mingcong Zeng) in the spectral sequence chart of
Figure 16, namely a
missing d_{11}, d_{7}
and d_{13} originating in dimensions 32, 36 and 37.
The corrected chart is here.
 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):289317.
 On the 3primary
ArfKervaire invariant problem (with M. Hill and M. Hopkins), in
preparation.

Remembering Mark Mahowald 19312013. Notices of
Amer. Math. Soc. 63 (2016),
652656. Unabridged
version.
 The cohomology
of C_{2}equivariant A(1) and the homotopy
of ko_{C2} (with B. J. Guillou,
M. Hill and D. C. Isaksen), Tunisian Journal of Mathematics,
3 (2020), 567632.
 The connective Morava Ktheory of the second mod p EilenbergMacLane space (with D. M. Davis and
W. S. Wilson), to appear.
 What is an infinitycategory?
Graduate Journal of Mathematics, Volume 8, Issue 2 (2023).
Return to Ravenel's home page
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