HarvardMIT Summer Seminar on the Kervaire Invariant
HarvardMIT Summer Seminar on the Kervaire Invariant
This webpage reflects activities of the NSF funded Summer Workshop in Algebraic
Topology.
Visitors
Idar Hansen, Trondheim: January 10  June 30
Mike Hill, UVA: June 1  August 31
Mehdi Kohrami, Wesleyan: June 1  August 31
Brooke Shipley, UIUC: July 3  July 6
Dave Carchedi, Utrecht: July 16  September 14
DenisCharles Cisinski: Paris 13: July 17  July 31
David Blanc, Haifa: July 18  August 31
Jim Turner, Grand Rapids: July 20  July 22
Doug Ravenel, Rochester: July 27  July 31, Aug 4  10
Sam Isaacson, London, Ont.: July 27  Aug 3
Mark Mahowald, Northwestern: Aug 4  Aug 10
David Ayala, Copenhagen: Aug 5  13, Aug 21  Sep 9, Sep 16  Sep 30
Jeff Smith, Vancouver: Aug 7  Aug 17
Jean Lannes, Paris: Aug 23  Sept 3
Seminar
This summer the seminar will focus on the Kervaire invariant, working up to an
exposition of the recent proof of the nonexistence of elements of
Kervaire invariant one by
Mike Hill, Mike Hopkins, and Doug Ravenel.
 When: Most Wednesdays, 3:005:00
 Where: MIT, room 2131, 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, 3:005:00, MIT 2131
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 by Haynes Miller
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
DenisCharles Cisinski, Paris 13
Notes

Monday, July 27, 3:00  4:00, MIT Room 2131
Invariance of Ktheory under derived equivalences
DenisCharles Cisinski, Paris 13

July 29:
The periodicity theorem in the solution to the ArfKervaire 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 Gspheres
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) 157186. Available from
JSTOR.

E.H. Brown, Jr., Generalizations of the Kervaire invariant, Annals of Math.
95 (1972), 368383. 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) 183197.
here

M.G.Barratt and H.R. Miller, On the antiautomorphism of the Steenrod algebra,
Cont. Math. 12 (1982) 4752.
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.