Discrete Morse theory for computing cellular sheaf cohomology

23 Dec 2013  ·  Justin Curry, Robert Ghrist, Vidit Nanda ·

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic techniques. As a consequence, we derive efficient techniques for distributed computation of (ordinary) cohomology of a cell complex.

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Algebraic Topology 55-04