On multiplicity of mappings between surfaces
| Autor: | Bogatyi, Semeon, Fricke, Jan, Kudryavtseva, Elena |
|---|---|
| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Geom. Topol. Monogr. 14 (2008) 49-62 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/gtm.2008.14.49 |
| Popis: | Let M and N be two closed (not necessarily orientable) surfaces, and f a continuous map from M to N. By definition, the minimal multiplicity MMR[f] of the map f denotes the minimal integer k having the following property: f can be deformed into a map g such that the number |g^{-1}(c)| of preimages of any point c in N under g is at most k. We calculate MMR[f] for any map $f$ of positive absolute degree A(f). The answer is formulated in terms of A(f), [pi_1(N):f_#(pi_1(M))], and the Euler characteristics of M and N. For a map f with A(f)=0, we prove the inequalities 2 <= MMR[f] <= 4. Comment: This is the version published by Geometry & Topology Monographs on 29 April 2008 |
| Databáze: | arXiv |
| Externí odkaz: |
|