FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 5, PAGES 209-223

**A topological version of the argument principle and Rouche's
theorem**

E. G. Sklyarenko

Abstract

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In this paper, the topological nature of the well-known in
multidimensional complex analysis generalization of the classic
argument principle is discussed.
The topological approach offered here, ensures some topological
results on the structure of pole and zero sets of holomorphic maps of
bounded domains in complex manifolds.
Some connections with integral representations of holomorphic
functions are studied and a geometric interpretation of the
Martinelli--Bochner complex-valued differential-form realization is
given.

Location: http://mech.math.msu.su/~fpm/eng/k05/k055/k05516h.htm

Last modified: February 26, 2006