General Overview of Cell Complexes

  • Lydia Olabisi, Ms. Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi
Keywords: Topological space, Cell complex, Homotopy, Simplicial Complex, CW Complex, Subcomplex, Simplex, Cells


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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