On generalized winding numbers
| dc.creator | Chernov, Vladimir | |
| dc.creator | Rudyak, Yuli B. | |
| dc.date | 2003-01-11 | |
| dc.date | 2006-11-09 | |
| dc.date.accessioned | 2026-07-07T06:35:34Z | |
| dc.date.available | 2026-07-07T06:35:34Z | |
| dc.description | 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 $f:N^{m-1} \to M^m, p \not\in Im f,$ we introduce an invariant $awin_p(f)$ that can be regarded as a generalization of the classical winding number of a planar curve around a point. We show that $awin_p$ estimates from below the number of times a wave front on $M$ passed through a given point $p\in M$ between two moments of time. Invariant $awin_p$ allows us to formulate the analogue of the complex analysis Cauchy integral formula for meromorphic functions on complex surfaces of genus bigger than one. | |
| dc.description | 13 pages, 1 figure The style of the paper is very significantly revised | |
| dc.identifier | https://arxiv.org/abs/math/0301117 | |
| dc.identifier | http://arxiv.org/abs/math/0301117 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99829 | |
| dc.subject | Geometric Topology | |
| dc.subject | Mathematical Physics | |
| dc.subject | Primary 55M25; Secondary 53Z05, 57R35 | |
| dc.title | On generalized winding numbers | |
| dc.type | text |