Homology Theory and Abelianization
- 1.8k Downloads
With hindsight, one can say that homology theory began with the Descartes-Euler polyhedron formula (1.3.8). It took a further step with Riemann’s definition of the connectivity of a surface, and the generalization to higher-dimensional connectivities by Betti 1871. All these results have to do with the computation of numerical invariants of a manifold by means of decomposition into “cells”; the computations involve only the numbers of cells and the incidence relations between them, and it is shown that certain numbers are independent of the particular cellular subdivision chosen.
KeywordsAbelian Group Homology Group Betti Number Finite Order Structure Theorem
Unable to display preview. Download preview PDF.