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

Abstract

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

References

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W. Rudin, Real and Complex Analysis. McGraw-Hill Book Co., Singapore, third ed., 1987.

T. tom Dieck, Algebraic topology. European Mathematical Society, 2008.

P. A. Suciu, MATH 4565 Topology Handout,. Department of Mathematics, Northeastern University, Boston, MA, 02115, 2016.
Published
2019-06-24