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Riemann Surfaces$
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Riemann Surfaces

Simon Donaldson

Print publication date: 2011

Print ISBN-13: 9780198526391

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198526391.001.0001

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Applications of the Euler characteristic

Applications of the Euler characteristic

Chapter:
(p.97) 7 Applications of the Euler characteristic
Source:
Riemann Surfaces
Author(s):

Simon Donaldson

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198526391.003.0007

The genus of a compact oriented smooth surface S can be defined as one-half the dimension of the de Rham cohomology group H 1(S). Another way of defining the genus involves the use of the Euler characteristic. This can be done via triangulations of the surface. This chapter describes this approach and then develops some applications.

Keywords:   smooth surface, genus, Euler characteristic, triangulations

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