References

• J. Milnor, The Steenrod algebra and its dual, Ann. of Math 67, 1958. MR0099653
• J. Milnor and J. Moore, On the structure of Hopf algebras, Ann. of Math 81, 1965. MR0174052
• G. Segal, The multiplicative group of classical cohomology, Quart. J. Math. Oxford Ser., 26, 1975. MR0380770
• S. R. Bullett and I. G. Macdonald, On the Adem relations, Topology 21, 1982. MR0649764
• A. Kozlowski, The transfer in Segal's cohomology, Illinois J. Math. 27, 1983. MR0720098
• R. M. W. Wood, Problems in the Steenrod algebra, Bull. London Math. Soc 30, no. 5, 1998. MR1643834
• M. Inoue, Odd primary Steenrod algebra, additive formal group laws, and modular invariants, J. Math. Soc. Japan 58, 2006. MR2228561
• J. McCleary, A user's guide to spectral sequences, 2nd edition, Cambridge Studes in Advanced Mathematics, 58, 2001.
• R. Mosher and M. Tangora, Cohomology operations and applications in homotopy theory, Dover, 2008.
• H. Miller, 1989 "Vector Fields on Spheres" course notes (notes by Matt Ando). Handwritten parts 1 and 2 or TeXed (by Eric Peterson).
• M. Hopkins, 1999 COCTALOS course notes.

Pictures of the subalgebra A(2): Computer drawn by Andre Henriques, and hand drawn by me. Also, the matching picture of A(2)/Sq¹.

Our theme for this summer is topics related to the Steenrod Algebra. Some topics of interest left to cover are

• ✓ Construction of the Steenrod Operations
• ✓ Computation of the cohomology of Eilenberg-Mac Lane spaces
• ✓ Discussion of Hopf algebras and the structure of the Steenrod algebra
• ✓ The Adem relations
• Vector fields on spheres, Hopf invariant 1
• ✓ The Adams spectral sequence

Notes:

• B. Guillou, Talk 1 (6/2/11). Construction of the Steenrod operations, Part 1.
  
• B. Guillou, Talk 2 (6/9/11). Construction of the Steenrod operations, Part 2.
  
• N. Aramian, Talk 3 (6/16/11). The cohomology of Eilenberg-Mac Lane spaces.
  
• M. Frankland, Talk 4 (6/23/11). The Steenrod Algebra and its Dual, Part 1. Sections 1-4 of Milnor's paper.
  
• S. Yeakel, Talk 5 (6/30/11). The Cohomology of Eilenberg-Mac Lane spaces as A-modules and stable splittings. Hatcher, section 4.L.
• N. Aramian, Talk 6 (7/8/11). The Steenrod Algebra and its Dual, Part 2. Sections 5-6 of Milnor's paper.
• P. Nelson, Talk 7 (7/14/11). The Adem Relations, following Bullett-MacDonald (and Miller's Notes).
• N. Stapleton, Talk 8 (7/21/11). The Steenrod Algebra and the Additive Formal Group Law.
• B. Guillou, Talk 9 (7/28/11). The Subalgebras A(n) and Nilpotence in the Steenrod Algebra.
• N. Aramian, Talk 10 (8/11/11). The Adams spectral sequence.

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