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Algebra i Analiz, 2008, Volume 20, Issue 5, Pages 217–233 (Mi aa538)  

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
Full-text PDF (262 kB) Citations (1)
References:
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
English version:
St. Petersburg Mathematical Journal, 2009, Volume 20, Issue 5, Pages 837–849
DOI: https://doi.org/10.1090/S1061-0022-09-01075-9
Bibliographic databases:
Document Type: Article
MSC: Primary 55M25; Secondary 53Z05, 57R35
Language: English
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
Citation in format AMSBIB
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\by V.~V.~Chernov (Tchernov), Y.~B.~Rudyak
\paper On generalized winding numbers
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 5
\pages 217--233
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2492365}
\zmath{https://zbmath.org/?q=an:1206.57031}
\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 5
\pages 837--849
\crossref{https://doi.org/10.1090/S1061-0022-09-01075-9}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000270134200009}
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  • https://www.mathnet.ru/eng/aa538
  • https://www.mathnet.ru/eng/aa/v20/i5/p217
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    References:53
    First page:8
     
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