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- W1978975028 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 $f : N^{m-1} {to } M^m, pnotin operatorname {Im} f$, an invariant $mathrm {awin}_p(f)$ 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 $mathrm {awin}_p$ estimates from below the number of passages of a wave front on $M$ through a given point $pin M$ between two moments of time. The invariant $mathrm {awin}_p$ makes it possible to formulate an analog of the complex analysis Cauchy integral formula for meromorphic functions on complex surfaces of genus exceeding one." @default.
- W1978975028 created "2016-06-24" @default.
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- W1978975028 date "2009-07-21" @default.
- W1978975028 modified "2023-10-18" @default.
- W1978975028 title "On generalized winding numbers" @default.
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- W1978975028 doi "https://doi.org/10.1090/s1061-0022-09-01075-9" @default.
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