-*- 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.

=============================================================================

Proposed by: Uli Walther <walther@math.purdue.edu>, 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:

