#6750: [with spkg, positive review] New version of optional Group Cohomology
spkg
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Reporter: SimonKing | Owner: SimonKing
Type: enhancement | Status: assigned
Priority: major | Milestone:
Component: optional packages | Keywords: cohomology ring p-group
Reviewer: | Author: Simon King
Merged: |
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Comment(by jhpalmieri):
Replying to [comment:43 SimonKing]:
> Dear John,
>
> Replying to [comment:42 jhpalmieri]:
> > There is a theorem for it. Look in ''Complex cobordism and stable
homotopy groups of spheres'' by Ravenel, Appendix A1.4.
> > According to A1.4.6, up to a sign, b<x1, x2, ...> is contained in
<bx1, x2, ...>, and similarly for the last position.
>
> Thank you for your hint!
>
> Ravenel says "In most cases the first page or two of the file is blank.
These files are in the process of being revised and should not be quoted
publicly."
>
> So, it seems that I can not cite the theorems from his book. Or is the
numbering in the printed version the same?
The numbering I gave you is from the first edition of the book; the
numbering in the on-line version is from a pre-print of the second
edition, which has now been published. I would guess that the numbering
is probably the same in the published version of the second edition, but
you could also just say "Section A1.4".
> > There is also an addition formula: see A1.4.5 in Ravenel. If you can
provide doctests for some of these in some examples, that would be great.
>
> This theorem refers to the matric Massey product. If I understand
correctly (but I am not an expert) what I implemented is not the matric
version of the Massey products. So, can you explain how I can create an
example out of Addition Theorem?
You're right, I'm not sure what to do with the matrices there. But
doctests for the juggling theorem are great -- thanks!
I'm not good enough with group cohomology to come up with other examples
to test this out; I think your doctests (and the evidence of the success
of the juggling theorems) is enough for me to give this a positive review.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6750#comment:45>
Sage <http://sagemath.org/>
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