Chapter 9. Algebraic, Difference and Geometric Topology

Table of Contents

Euler formula
Homology and Cohomology
Homotopy
Cohomology with Coefficients
Exact Sequences
Homology Spheres
ToDo

You possibly already know the Euler formula (Equation 9.1, “Euler formula”) in three dimensions (v: vertices, e: edges, f: faces, g: genus, 2 - 2g: Euler characteristic):


The genus is a topologic invariant property of the surface. It is defined as the largest number of non-intersecting simple closed curves that can be drawn without separating it. In cases with boundaries holes count as normal faces in fulfilling the Euler formula.