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Invariants of Stable Maps between Closed Orientable Surfaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Catarina Mendes de Jesus S. & Pantaleón D. Romero, 2021. "Invariants of Stable Maps between Closed Orientable Surfaces," Mathematics, MDPI, vol. 9(3), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:215-:d:484697
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    Cited by:

    1. Catarina Mendes de Jesus & Pantaleón D. Romero, 2022. "Graphs of Stable Gauss Maps and Quine’s Theorem for Oriented 2-Manifolds," Mathematics, MDPI, vol. 10(17), pages 1-11, August.

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