This quantity can be defined on a finite CW complex as an alternating sum, and an extension of this quantity to higher dimensions can be obtained through Betti numbers.
This quantity can be defined on a finite CW complex as an alternating sum, and an extension of this quantity to higher dimensions can be obtained through Betti numbers. Examining the trace of the matrix for a map homotopic to the identity shows that this quantity for such maps is equal to the Lefschetz number. It can be determined by taking the number of maxima and minima and subtracting saddle points or by subtracting twice the genus from two, and Poincare's formula for polyhedra gives it by subtracting the number of edges and faces from the number of vertices. For 10 points, what is this property of a compacted, closed surface that is zero for the Klein bottle and M?bius strip and positive 2 for a sphere, and which was first introduced by its namesake in his solution to the "bridges of Konigsberg" problem.
This quantity can be defined on a finite CW complex as an alternating sum, and an extension of this quantity to higher dimensions can be obtained through Betti numbers.
Euler-Poincar?characteristic or number