Harvard-MIT Summer Seminar on the Kervaire Invariant

Visitors

Seminar

• When: Most Wednesdays, 3:00--5:00
• Where: MIT, room 2-131, and perhaps at Harvard.
• Who: The seminar is being organized by Mike Hopkins and Haynes Miller.

Schedule of talks:

• May 27:
  The Kevaire invariant as surgery obstruction, I
  Ben Wieland, Brown University
  
  
• Monday, June 1, 3:00--5:00, MIT 2-131
  The Kervaire invariant as surgery obstruction, II
  Ben Wieland, Brown University
  
  
• June 3: no meeting
  
  
• June 10: no meeting
  
  
• June 17:
  Quadratic refinements, after Browder and Brown
  Jacob Lurie, MIT
  Notes
  
  
• June 24:
  Browder's theorem and manifolds with corners
  Haynes Miller, MIT
  Script
  
  
• July 1:
  The Kervaire invariant and the Whitehead square
  Martin Frankland, MIT
  Script
  Comment on the Adams differential
  
  
• July 8:
  Complex bordism and the Kervaire invariant
  Mike Hopkins, Harvard
  Notes
  
  
• July 15:
  Computations with the slice spectral sequence: gaps and periodicity
  Mike Hill, Harvard
  Notes
  
  
• July 22:
  Homotopy weakening of algebras
  Denis-Charles Cisinski, Paris 13
  Notes
  
  
• Monday, July 27, 3:00 - 4:00, MIT Room 2-131
  Invariance of K-theory under derived equivalences
  Denis-Charles Cisinski, Paris 13
  
  
• July 29:
  The periodicity theorem in the solution to the Arf-Kervaire invariant problem
  Doug Ravenel, Rochester
  Slides, Script
  
  
• Monday, August 10, 3:00, Harvard Science Center 507
  Homotopy theory of the Kervaire invariant
  Mark Mahowald, Northwestern
  
  
• August 12:
  Moduli spaces of homotopy G-spheres
  Jeff Smith, University of British Columbia
  Notes by Olga Stroilova.
  
  
• August 26:
  The Kervaire invariant and manifolds with boundary
  Jean Lannes, Ecole Polytechnique
  
  
  Thanks to Angelica Osorno for the lecture notes.

Some references:

Here are citations or scans of some relevant documents.


• E.H. Brown, Jr., and F.P. Peterson, Whitehead products and cohomology operations, Quart. J. Math. Oxford (2) 15 (1964). here
  
  
• W. Browder, The Kervaire invariant of framed manifolds and its generalization, Annals of Math. 90 (1969) 157--186. Available from JSTOR.
  
  
• E.H. Brown, Jr., Generalizations of the Kervaire invariant, Annals of Math. 95 (1972), 368--383. Available from JSTOR.
  
  
• M.E. Mahowald, Some remarks on the Kervaire invariant problem from the homtopy point of view, Algebraic Topology, Proceedings of Symposia in Pure Mathematics XXII, AMS, 1971. here
  
  
• J.E. Lannes, Sur l'invariant de Kervaire des varietes fermees stablement parallelisees, Ann. Sci. E.N.S. 14 (1981) 183--197. here
  
  
• M.G.Barratt and H.R. Miller, On the anti-automorphism of the Steenrod algebra, Cont. Math. 12 (1982) 47--52. here
  
  
• M.G. Barratt, J.D.S. Jones, and M.E. Mahowald, The Kervaire invariant problem, Proceedings of the Northwestern Homotopy Theory Conference, Contemp. Math. 19, AMS, 1983. here
  
  
• M.G. Barratt, J.D.S. Jones, and M.E. Mahowald, The Kervaire invariant and the Hopf invariant, Algebraic Topology, Seattle, 1985, Springer Lecture Notes in Math. 1286. here
  
  
• R.L. Cohen, J.D.S.Jones, and M.E. Mahowald, The Kervaire invariant of immersions, Inv. math. 79 (1985). here
  
  
• F.R. Cohen, A course in some aspects of classical homotopy theory, Algebraic Topology, Seattle, 1985, Springer Lecture Notes in Math. 1286. excerpt
  
  
• H.R. Miller and D.C. Ravenel, Mark Mahowald's work on the homotopy groups of spheres, Algebraic Topology, Oaxtepec 1991, Contemporary Math. 146, 1993. here
  
  
• Doug Ravenel's website contains more references, and links to slides from his talks in Lisbon.