Invariants of Stable Maps between Closed Orientable Surfaces

Invariants of Stable Maps between Closed Orientable Surfaces

In this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces <i>M</i> and <i>N</i> with a given branch set of curves immersed on <i>N</i>. We will study, from a global point of view, the behavior of its families in...

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Main Authors: Catarina Mendes de Jesus S., Pantaleón D. Romero
Format: Article
Language:English
Published: MDPI AG 2021-01-01
Series:Mathematics
Subjects:
cusps
graphs
degree
Euler characteristic
stable maps
Online Access:https://www.mdpi.com/2227-7390/9/3/215
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spelling doaj-948d2f786f4e41699cf54b8d9923e2562021-01-22T00:05:45ZengMDPI AGMathematics2227-73902021-01-01921521510.3390/math9030215Invariants of Stable Maps between Closed Orientable SurfacesCatarina Mendes de Jesus S.0Pantaleón D. Romero1Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora 36036-900, BrazilESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias, Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, 46115 Alfara del Patriarca, SpainIn this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces <i>M</i> and <i>N</i> with a given branch set of curves immersed on <i>N</i>. We will study, from a global point of view, the behavior of its families in different isotopies classes on the space of smooth maps. The main goal is to obtain different relationships between invariants. We will provide a new proof of Quine’s Theorem.https://www.mdpi.com/2227-7390/9/3/215cuspsgraphsdegreeEuler characteristicstable maps
collection DOAJ
language English
format Article
sources DOAJ
author Catarina Mendes de Jesus S.
Pantaleón D. Romero
spellingShingle Catarina Mendes de Jesus S.
Pantaleón D. Romero
Invariants of Stable Maps between Closed Orientable Surfaces
Mathematics
cusps
graphs
degree
Euler characteristic
stable maps
author_facet Catarina Mendes de Jesus S.
Pantaleón D. Romero
author_sort Catarina Mendes de Jesus S.
title Invariants of Stable Maps between Closed Orientable Surfaces
title_short Invariants of Stable Maps between Closed Orientable Surfaces
title_full Invariants of Stable Maps between Closed Orientable Surfaces
title_fullStr Invariants of Stable Maps between Closed Orientable Surfaces
title_full_unstemmed Invariants of Stable Maps between Closed Orientable Surfaces
title_sort invariants of stable maps between closed orientable surfaces
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-01-01
description In this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces <i>M</i> and <i>N</i> with a given branch set of curves immersed on <i>N</i>. We will study, from a global point of view, the behavior of its families in different isotopies classes on the space of smooth maps. The main goal is to obtain different relationships between invariants. We will provide a new proof of Quine’s Theorem.
topic cusps
graphs
degree
Euler characteristic
stable maps
url https://www.mdpi.com/2227-7390/9/3/215
work_keys_str_mv AT catarinamendesdejesuss invariantsofstablemapsbetweenclosedorientablesurfaces
AT pantaleondromero invariantsofstablemapsbetweenclosedorientablesurfaces
_version_ 1724329437738041344

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