Abstract
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Given closed possibly nonorientable surfaces
,
, we prove that
if a map
has
geometric degree
,
then
.
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 factorization theorem of
Edmonds, a simple natural proof of which is also presented.
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Keywords
surfaces, geometric degree, branched covering
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Mathematical Subject Classification
Primary: 57K20
Secondary: 55M25
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Milestones
Received: 16 August 2023
Revised: 11 February 2024
Accepted: 2 March 2024
Published: 16 April 2024
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| © 2024 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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