Homology of Klein bottle
This article describes the value (and the process used to compute it) of some homotopy invariant(s) for a topological space or family of topological spaces. The invariant is homology and the topological space/family is Klein bottle
Get more specific information about Klein bottle | Get more computations of homology
The homology of the Klein bottle is given by:
All other homology groups are 0.
These are all invariants that can be computed in terms of the homology groups.
|Invariant||General description||Description of value for Klein bottle|
|Betti numbers||The Betti number is the rank of the homology group.||, for|
|Poincare polynomial||Generating polynomial for Betti numbers|
|Euler characteristic||0 -- consistent with the fact that its double cover is the 2-torus, which, being a nontrivial compact connected Lie group, has Euler characteristic zero, and the fact that Euler characteristic of covering space is product of degree of covering and Euler characteristic of base|