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تسجيل

Acyclic Chain Complex

المؤلف:  Ranicki, A.

المصدر:  "Notes on Reidemeister Torsion." 1997. https://www.maths.ed.ac.uk/~aar/papers/torsion.pdf.

الجزء والصفحة:  ...

5-5-2021

2802

Acyclic Chain Complex

Let  be a commutative ring and let  be an R-module for . A chain complex  of the form

is said to be acyclic if its th homology group  is trivial for all values .

A straightforward result in homological algebra states that a chain complex  with each  free is acyclic if and only if there exists a chain contraction .

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REFERENCES:

Ranicki, A. "Notes on Reidemeister Torsion." 1997. https://www.maths.ed.ac.uk/~aar/papers/torsion.pdf.