On multiplicity of mappings between surfaces
| dc.creator | Bogatyi, Semeon | |
| dc.creator | Fricke, Jan | |
| dc.creator | Kudryavtseva, Elena | |
| dc.date | 2009-04-07 | |
| dc.date.accessioned | 2026-07-07T13:01:21Z | |
| dc.date.available | 2026-07-07T13:01:21Z | |
| dc.description | 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. | |
| dc.description | This is the version published by Geometry & Topology Monographs on 29 April 2008 | |
| dc.identifier | https://arxiv.org/abs/0904.1197 | |
| dc.identifier | http://arxiv.org/abs/0904.1197 | |
| dc.identifier | Geom. Topol. Monogr. 14 (2008) 49-62 | |
| dc.identifier | doi:10.2140/gtm.2008.14.49 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226123 | |
| dc.subject | Geometric Topology | |
| dc.subject | 54H25, 55M20, 57M12 | |
| dc.title | On multiplicity of mappings between surfaces | |
| dc.type | text |