nLab Doug Ravenel

• webpage

• Michael Hopkins, The mathematical work of Douglas C. Ravenel, Homology Homotopy Appl. Volume 10, Number 3 (2008), 1-13 (euclid:hha/1251832464)

Selected writings

On the Hopf ring of MU:

• Douglas Ravenel, W. Stephen Wilson, The Hopf ring for complex cobordism, Bull. Amer. Math. Soc. 80 (6) 1185 - 1189, November 1974 (doi:10.1016/0022-4049(77)90070-6, euclid, pdf)

On the Adams-Novikov spectral sequence:

• Douglas Ravenel, A Novice’s guide to the Adams-Novikov spectral sequence, in: Michael Barratt, Mark Mahowald (eds.) Geometric Applications of Homotopy Theory II. Lecture Notes in Mathematics, vol 658, Springer 1978 (doi:10.1007/BFb0068728, pdf)

On chromatic homotopy theory and introducing Ravenel's spectra and Ravenel's conjectures:

• Douglas Ravenel, Localization with Respect to Certain Periodic Homology Theories, American Journal of Mathematics Vol. 106, No. 2 (Apr., 1984), pp. 351-414 (doi:10.2307/2374308, jstor:2374308)

On stable homotopy groups of spheres and chromatic homotopy theory:

• Mark Mahowald, Doug Ravenel, Towards a Global Understanding of the Homotopy Groups of Spheres, in: Samuel Gitler (ed.): The Lefschetz Centennial Conference: Proceedings on Algebraic Topology II, Contemporary Mathematics volume 58, AMS 1987 (ISBN:978-0-8218-5063-3, pdf, pdf)

On stable homotopy groups of spheres and chromatic homotopy theory:

• Doug Ravenel, Nilpotence and Periodicity in Stable Homotopy Theory, Annals of Mathematics Studies 128, Princeton University Press (1992) [ISBN:9780691025728, pdf, webpage]

  (“the orange book”)

On elliptic genera:

• Peter Landweber, Douglas Ravenel, Robert Stong, Periodic cohomology theories defined by elliptic curves, in Haynes Miller et al (eds.), The Cech centennial: A conference on homotopy theory, June 1993, AMS (1995) (pdf)

On chromatic homotopy theory, complex cobordism cohomology and stable homotopy groups of spheres,:

• Doug Ravenel, Complex cobordism and stable homotopy groups of spheres, Academic Press Orland (1986) reprinted as: AMS Chelsea Publishing, Volume 347, 2004 (ISBN:978-0-8218-2967-7, webpage, pdf)

On the Morava K-theory of iterated loop spaces of spheres and on stable splitting of mapping spaces:

• Douglas Ravenel, What we still don’t know about loop spaces of spheres, in: Mark Mahowald, Stewart Priddy (eds.), Homotopy Theory via Algebraic Geometry and Group Representations, Contemporary Mathematics 220, AMS 1998 (pdf, pdf, doi:10.1090/conm/220)

On generalized (transchromatic) group characters via complex oriented cohomology theory:

• Michael Hopkins, Nicholas Kuhn, Douglas Ravenel, Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc. 13 (2000) 553-594 [doi:10.1090/S0894-0347-00-00332-5, pdf]

Solving the Arf-Kervaire invariant problem with methods of equivariant stable homotopy theory:

• Michael Hill, Michael Hopkins, Douglas Ravenel, Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem, New Mathematical Monographs, Cambridge University Press (2021) [doi:10.1017/9781108917278]

• Michael Hill, Michael Hopkins, Douglas Ravenel, On the non-existence of elements of Kervaire invariant one, Annals of Mathematics 184 1 (2016)[doi:10.4007/annals.2016.184.1.1, arXiv:0908.3724, talk slides]

• Michael Hill, Michael Hopkins, Douglas Ravenel, The Arf-Kervaire problem in algebraic topology: Sketch of the proof, Current Developments in Mathematics, 2010: 1-44 (2011) (pdf, doi:10.4310/CDM.2010.v2010.n1.a1)

• Michael Hill, Michael Hopkins, Douglas Ravenel, The Arf-Kervaire invariant problem in algebraic topology: introduction (2016) [pdf]

category: people