Handwritten lecture notes
and links shown in class 
Monday 
Wednesday 
Friday April 30,
2010 DCR notes: Completion of the
proof of the Reduction Theorem and recap of the course. The
odd primary Kervaire invariant theorem is the subject of Section 6.4
of the
green book and
of my
1978 paper.

April 26, 2010 DCR notes:
The proof of the Reduction Theorem I. Proofs of some of
the assertions made today can be found in Section 4 of the HHR
preprint. 
April 28, 2010 DCR notes:
The proof of the Reduction Theorem II. The numbered statements here appear in the HHR
preprint.
Picture of the slice spectral sequence referred to on page 10. It
is also shown on page 76 of
the preprint. 
Thursday April 22,
2010 DCR notes: The formal part of
the Slice Theorem. This is a world premiere performance.

April 19, 2010 DCR notes:
More about the AdamsNovikov spectral sequence.
The structure theorems for the Hopf algebroids associated with MU and BP are stated and proved in Appendix 2 of the green book as A2.1.16 and A2.1.27. 
April 21, 2010 DCR notes:
The proof of the Detection Theorem.
See my 6th Tokyo lecture. 
April 12, 2010 DCR notes:
The Periodicity Theorem for C_{8}. This material can
be found in my Princeton lecture. 
April 14, 2010 DCR notes:
Toward the AdamsNovikov spectral sequence.
This material can be found in the green book,
specifically the second section of Chapter 2
and the first section of Appendix 1.
The first two pages of each of these files are blank; keep on clicking. 
April 5, 2010 DCR notes:
Toward the slice spectral sequence
for MU^{(4)}. The charts of the two
spectral sequences can be found towards the end of
Hill's Skye
handout. The pictures of the ρ_{8}slices
can be found on page 3 of my Princeton talk.

April 7, 2010 No class 
Friday April 2,
2010. DCR notes: The fixed point
theorem and some calculations with MU^{(4)}.
For the calculations, see the last 3 pages
of
my third Tokyo lecture. 
March 29, 2010 DCR notes:
The slice spectral sequence for MU. 
March 31, 2010 DCR notes:
More of the slice spectral sequence for MU and a
periodicity theorem. For a picture of the slice spectral
sequence for K_{R}, see the last page
of my
third Lisbon lecture. 
March 22, 2010 DCR notes: A
functorial definition of equivariant spectra. This is a
reinterpretation of the definition
of MandellMay. 
March 24, 2010 DCR notes: Setting up the slice spectral sequence.
This is similar to my 4th Tokyo lecture. 
March 15, 2010 DCR notes:
Equivariant spaces and spectra.
See pages 58 of my second Lisbon lecture.
For deeper background, see
GreenleesMay. 
March 17, 2010 DCR notes:
More about equivariant spectra. 
March 1, 2010 DCR notes: Complex
cobordism and formal group laws. 
March 3, 2010 DCR notes: Formal
group laws and formal Amodules. Some of this material
can be found
in Appendix
2 of
the green
book. 
February 22, 2010 DCR notes:
More on the Adams spectral sequence and Browder's criterion. 
February 24, 2010 DCR notes:
Overview of the proof and an introduction to MUtheory 
February 15, 2010 DCR notes:
Toward the Adams spectral sequence. 
February 17, 2010 DCR notes:
Introduction to spectra.
Christian
Nassau's 210stem Ext chart 
February 8, 2010 No class 
February 10, 2010 No class 
February 1, 2010 DCR notes: KervaireMilnor's use of surgery to classify exotic spheres.
Hopkins' San Francisco slides
(20 MB file, be patient)
 Slide 32 shows surgery on the torus.
 Slide 38 shows the torus with twisted framing.
 Slide 53 shows Kervaire's example.

February 3, 2010
DCR notes: Review of the Kervaire
invariant problem and
introduction to Steenrod operations.

January 25, 2010
DCR notes: Framed cobordism and the definition of the Arf invariant.
The Turkish 10 Lira note 
January 27, 2010
DCR notes: Kervaire's construction of a nonsmoothable manifold and the Kervaire invariant problem. 
Holiday 
January 20, 2010
No notes available
Wikipedia article on the Kervaire invariant 