-*- 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 , 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 ============================================================================= Progress log: