Resources for Math 395, Spring 2009, "Classics Seminar in Topology"

General Information

Ralph's office hours: Mondays at 2 pm.

Assignments

1. Jeremy: Cohomology of Eilenberg-Mac Lane spaces.
2. Ilya: The Steenrod algebra and its dual.
3. Anssi: The Adams Spectral Sequence and unitary cobordism.
4. Nathan: Formal group laws.
5. Ulrik: The Brown-Peterson spectrum.
6. Eric and Joseph: Adams's "Hopf invariant one".
7. Robin: Vector fields on spheres.
8. Josh: The Kervaire invariant.

Past Talks

• 31 Mar: Ralph, introduction.
• 2 Apr: Ralph, Thom's computation of the homotopy type of the spectrum MO.
• 7 Apr: Jeremy, Serre's calculation of the cohomology of Eilenberg-Mac Lane spaces.
• 9 Apr: Jeremy, The Serre spectral sequence and Cartan's theorem.
• 14 Apr: No class.
• 16 Apr: Ilya, The Steenrod algebra and its dual.
• 21 Apr: Anssi, Construction of the Adams spectral sequence.
• 23 Apr: Anssi, Milnor's computation of the homotopy groups of the spectrum MU.
• 28 Apr: Nathan, Complex orientations for ring spectra and formal group laws.
• 30 Apr: Nathan, Quillen's ring isomorphism between the Lazard ring and the homotopy groups of MU.
• 5 May: Ralph, The Kervaire invariant.
• 7 May: Eric, Secondary cohomology operations.
• 12 May: Eric, Secondary cohomology operations, continued; Cohomology of the Steenrod algebra.
• 14 May: Joseph, Decomposition of higher dyadic Steenrod squares.

Upcoming Talks

• 19 May: Joseph, Decomposition of higher dyadic Steenrod squares.
• 21 May: Robin
• 26 May: Robin
• 28 May: Josh
• 2 Jun: Ulrik
• 4 Jun: Josh

Notes and References

• Notes of Gérald Gaudens on the Adams spectral sequence and the Kervaire invariant, courtesy of Bruce Williams.

Books and Papers

• Adams, J.F. "Vector fields on spheres." Ann. Math. 75 1962, 603–632. Available at JStor.
• Adams, J.F. "On the non-existence of elements of Hopf invariant one." Ann. Math. 72 1960, 20–104. Available at JStor. 2-up version here.
• Adams, J.F., Atiyah, M.F. "K-theory and the Hopf invariant." Quart. J. Math. 17 1966, 31–38. Available at Oxford Journals.
• Anderson, D.W., Brown, E.H., Jr., Peterson, F.P. "The structure of the Spin cobordism ring." Ann. Math. 86 1967, 271–298. Available at JStor.
• Browder, William. "The Kervaire invariant of framed manifolds and its generalization." Ann. Math. 90 1969, 157–186. Available at JStor.
• Brown, Edgar H., Jr., Peterson, Franklin P. "A spectrum whose Z_p cohomology is the algebra of reduced pth powers." Topology 5 1966, 149–154. Available at ScienceDirect.
• Milnor, J. "On the cobordism ring Ω^* and a complex analogue. I." Amer. J. Math. 82 1960, 505–521. Available at JStor.
• Milnor, J. "The Steenrod algebra and its dual." Ann. Math. 67 1958, 150–171. Available at JStor.
• Quillen, Daniel. "On the formal group laws of unoriented and complex cobordism theory." Bull. Amer. Math. Soc. 75 1969, 1293–1298. Available at the AMS.