Descriptive Cellular Homology
M.Z. Ahmad, J.F. Peters
TL;DR
This paper introduces a new form of cellular homology for cell complexes, extending CW topology, and demonstrates its application in analyzing shape persistence in fiber bundles.
Contribution
It develops descriptive cellular homology, linking cellular complexes to fiber bundle topologies, and applies it to shape persistence analysis in CW spaces.
Findings
Descriptive cellular homology extends CW topology to cell complexes.
A descriptive cellular complex defines a topology on fibers in fiber bundles.
Application to shape persistence demonstrates practical utility.
Abstract
This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular complex is a topology on fibres in a fibre bundle. An application of two forms of cellular homology is given in terms of the persistence of shapes in CW spaces.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Topological and Geometric Data Analysis