General Overview of Cell Complexes
A very large class of topological spaces of practical interest can be represented by a decomposition into subsets, each with simple topology, glued
together along their boundaries. A decomposition of this form is commonly called a cell complex. Abstract graphs (as branched 1-manifolds) are examples of cell complexes, as are quadrilateral and hexahedral meshes, and 3d
triangulations supporting normal surfaces. There are several different ways to formalize the intuitive notion of a ’cell complex’, striking different balances between simplicity and generality. I’ll describe different definitions and how they are interconnected
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