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This article is cited in 1 scientific paper (total in 1 paper)
Research Papers
On generalized winding numbers
V. V. Chernov (Tchernov)a, Y. B. Rudyakb a Department of Mathematics, Dartmouth College, Hanover NH, USA
b Department of Mathematics, University of Florida, Gainesvill, FL, USA
Abstract:
Let $M^m$ be an oriented manifold, let $N^{m-1}$ be an oriented closed manifold, and let $p$ be a point in $M^m$. For a smooth map $f\colon N^{m-1}\to M^m$, $p\notin\operatorname{Im}f$, an invariant $\operatorname{awin}_p(f)$ is introduced, which can be regarded as a generalization of the classical winding number of a planar curve around a point. It is shown that $\operatorname{awin}_p$ estimates from below the number of passages of a wave front on $M$ through a given point $p\in M$ between two moments of time. The invariant $\operatorname{awin}_p$ makes it possible to formulate an analog of the complex analysis Cauchy integral formula for meromorphic functions on complex surfaces of genus exceeding one.
Keywords:
Affine winding number, linking number, invariant.
Received: 14.11.2006
Citation:
V. V. Chernov (Tchernov), Y. B. Rudyak, “On generalized winding numbers”, Algebra i Analiz, 20:5 (2008), 217–233; St. Petersburg Math. J., 20:5 (2009), 837–849
Linking options:
https://www.mathnet.ru/eng/aa538 https://www.mathnet.ru/eng/aa/v20/i5/p217
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Abstract page: | 395 | Full-text PDF : | 98 | References: | 53 | First page: | 8 |
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