Construction of vector fields and foliations on surfaces
by Wing-sum Chan
THESIS
1997
M.Phil. Mathematics
x, 73 leaves : ill. ; 30 cm
Abstract
The famous Poincare-Hopf Index Theorem asserts that the sum of the indices of the singularities of a vector field v[?] (or more generally, a foliation F) on a closed surface M is independent of v[?] (or F) and solely depends on the topology of M. In fact, it is precisely the Euler-Poincare characteristic of M. This paper trys to prove the converse of it and generalises the results to the case M has nonempty boundary by explicit constructions.
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