Invariants of Stable Maps between Closed Orientable Surfaces

Catarina Mendes de Jesus S. and Pantaleón D. Romero
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Catarina Mendes de Jesus S.: Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora 36036-900, Brazil
Pantaleón D. Romero: ESI International Chair@CEU-UCH, Departamento de Matemáticas, Física y Ciencias, Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, 46115 Alfara del Patriarca, Spain

Mathematics, 2021, vol. 9, issue 3, 1-11

Abstract: In this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces M and N with a given branch set of curves immersed on N . 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.

Keywords: cusps; graphs; degree; Euler characteristic; stable maps (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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