Euler characteristic
The term Euler characteristic is defined for several objects.
If is a finite simplicial complex of dimension , let be the number of simplexes of dimension . The Euler characteristic of is defined to be
Next, if is a finite CW complex, let be the number of i-cells in . The Euler characteristic of is defined to be
If is a finite polyhedron, with triangulation , a simplicial complex, then the Euler characteristic of is . It can be shown that all triangulations of have the same value for so that this is well-defined.
Finally, if is a finitely generated graded group, then the Euler characteristic of is defined to be
Title | Euler characteristic |
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Canonical name | EulerCharacteristic |
Date of creation | 2013-03-22 16:12:51 |
Last modified on | 2013-03-22 16:12:51 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 13 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 55N99 |