@article {MATHEDUC.05192618,
author = {Persson, Ulf},
title = {The Euler number. (Eulertalet.)},
year = {2006},
journal = {Normat. Nordisk Matematisk Tidskrift},
volume = {54},
number = {4},
issn = {0801-3500},
pages = {173-183},
publisher = {Nationellt Centrum f\"or Matematikutbildning, G\"oteborg},
abstract = {Summary: The Euler-number is often defined as the alternating sum of the Betti-numbers, or equivalently as the alternate sum of the number of simplices of a given dimension. The problem is that this requires an explicit triangulation. For purposes of actual computation it is much more efficient (and illuminating) to take a more ``functorial'' approach, namely the Euler-number which behaves like a cardinal number, but with the difference that we can freely mix dimensions. In the article this is illustrated by a variety of examples, compact real surfaces, projective spaces and Grassmannians, curves and hypersurfaces. We also show how to relate the Euler-number to the types of singularities of a vector field and to prove the Gauss-Bonnets formula, relating the integral of the Gaussian curvature to the Euler-number of the surface.},
msc2010 = {H70xx (I60xx G90xx I90xx)},
identifier = {2007b.00369},
}