A chain contraction 
of a chain complex 
over a commutative ring 
is a collection of R-module morphisms 
satisfying
 |
for all 
. Here, each 
is an R-module, and
the chain complex has the form
 |
The map 
is the boundary
operator of 
.
Chain Contraction
See also
Boundary Operator, Chain Complex, Commutative Ring, Module, Morphism, R-ModulePortions of this entry contributed by Christopher Stover
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References
Ranicki, A. "Notes on Reidemeister Torsion." 2001. https://webhomes.maths.ed.ac.uk/~v1ranick/papers/torsion.pdf.Referenced on Wolfram|Alpha
Chain ContractionCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Chain Contraction." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ChainContraction.html