On generalized winding numbers
Chernov, Vladimir ; Rudyak, Yuli B.
arXiv, 0301117 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-01-11
Classification:  Mathematics - Geometric Topology,  Mathematical Physics,  Primary 55M25,  Secondary 53Z05, 57R35 
@article{0301117,
     author = {Chernov, Vladimir and Rudyak, Yuli B.},
     title = {On generalized winding numbers},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0301117}
}

Chernov, Vladimir; Rudyak, Yuli B. On generalized winding numbers. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0301117/