Peer-Reviewed Journal Details
Mandatory Fields
Alokbi, N,Ellis, G
2018
January
Homology Homotopy And Applications
DISTRIBUTED COMPUTATION OF LOW-DIMENSIONAL CUP PRODUCTS
Published
()
Optional Fields
cohomology cup product digital image data analysis COHOMOLOGY COMPLEXES GROUPOIDS THEOREM SPACES
20
41
59
We describe a distributed algorithm for computing the cup product boolean OR : H-1(X, Z) x H-1(X, Z) -> H-2(X, Z) on the cohomology of a finite regular CW-space. A serial implementation of the algorithm is illustrated in two applied topological settings: (i) 3-dimensional digital images; (ii) topological data analysis of a finite sample of points from a metric space. For the second of these illustrations we introduce a cohomological enrichment of the Mapper clustering procedure which may be of independent interest.
10.4310/HHA.2018.v20.n2.a3
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