Hi!
To those interested in the cohomology of finite p-groups: There is a
new SPKG (version 1.2) at http://trac.sagemath.org/sage_trac/ticket/7195
The new stuff in it are bar codes. This was originally used to study
the geometric shape of point cloud data, but we use it to study
groups. Idea:
1. Take a normal series (e.g., Upper Central Series), yielding a
chain of inclusion and quotient maps.
2. Construct the chain of induced homomorphisms of cohomology rings.
3. Watch the cocycles die under the induced homomorphisms, and
document how many mappings they survive.
In each degree, this life time of cocycles is depicted by a collection
of bars of different length and number ("bar code"), which is
equivalent to a certain upper triangular integer matrix. Combining all
degrees, one gets an upper triangular matrix of rational functions
(Poincare series). The idea of using bar codes in group cohomology
seems to be new, and is due to Graham Ellis and myself.
It turns out that the bar codes are quite useful in distinguishing
groups. I give an example in the ticket description.
Best regards,
Simon
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