#6750: [with spkg, needs review] New version of optional Group Cohomology spkg
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Reporter: SimonKing | Owner: Simon King
Type: enhancement | Status: new
Priority: major | Milestone:
Component: optional packages | Keywords: cohomology ring p-group
Reviewer: | Author: Simon King
Merged: |
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Comment(by SimonKing):
Perhaps I should point out in more detail ''why'' I believe that an expert
for Steenrod actions might be able to provide good examples.
There is a general result of David Kraines, "Higher Products", Bulletin of
the AMS 72 (1966), Part 1:128-131.
__Theorem A (page 131)__
- Let p>2 be a prime.
- Let P^m^: H^q^(X;Z/p)->H^q+2m(p-1)^(X;Z/p) be the Steenrod pth power
operation.
- Let \beta denote the Bockstein operator associated with the exact
sequence of coefficient groups 0 —> Z/p -> Z/p^2^ -> Z/p -> 0
- Let u be an element of H^2m+1^(X;Z/p).
- Let <u>^p^ denote the p-fold restricted Massey product of a cocycle u
(as defined by Kraines, so it is a single cocycle, not a ''set'' of
cocycles).
Then <u>^p^ = - \beta P^m^(u)
In our spkg, one would compute this restricted p-fold Massey product by
{{{u.massey_power()}}}
I don't know of general results in the case of cocycles of even degree,
though.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6750#comment:6>
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