-*- M2 -*-
Title: Connecting Homomorphisms
Description: Write a package that compute connecting homomorphisms in the
homology of a short exact sequence 0 -> A -> B -> C -> 0 of chain complexes.
We already have mapping cones, so the problem is really to compose the map HH C
-> HH cone (B -> C) with the inverse of the isomorphism HH cone (A -> 0) -->
HH cone (B -> C).
In terms of that, implement the Bockstein operation for a chain complex C over
ZZ. It is the connecting homomorphism associated to the exact sequence 0 ->
C/n -> C/n^2 -> C/n -> 0, if C is free. If C is not free, replace C/n by
cone(n:C-->C), and similarly for n^2.
In terms of the code, one must make our functions "HH" and "cone" into
functors.
Maybe implement the derived category, too, so the connecting homomorphism is
obtainable by applying HH to a single object representing a map in the derived
category.
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Proposed by: Uli Walther , dan
Potential Advisor:
Project assigned to: Chris Cunningham, January, 2009.
Current status: some code has been written, but hasn't been checked into
the repository
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Progress log: