Maximal degree of a map of surfaces
Abstract
Given closed possibly nonorientable surfaces M,N, we prove that if a map f:M N has degree d>0, then (M) d·(N). We give all necessary comments on the definition and properties of geometric degree, which can be defined for any map. Our proof is based on the Kneser-Edmonds factorization theorem, simple natural proof of which is also presented.
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