Homology, Homotopy and Applications

Volume 24 (2022)

Number 2

Graphs associated to fold maps from closed surfaces to the projective plane

Pages: 221 – 240

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n2.a10

Authors

Catarina Mendes de Jesus Sánchez (Department of Mathematics, Federal University of Juiz de Fora, MG, Brazil)

Maria del Carmen Romero Fuster (Department of Mathematics, Universitat de València, Spain)

Abstract

We describe in this paper how to attach a weighted graph to any fold map (i.e., a stable map without cusps) with planar apparent contour from a closed surface to the projective plane. Also we study necessary and sufficient conditions for a weighted graph with non negatively weighted vertices to be the graph of a fold map from a closed surface to the projective plane.

Keywords

closed surface, graph, stable map

2010 Mathematics Subject Classification

37E25, 57R45, 57R65, 57R70

Received 6 February 2021

Received revised 6 September 2021

Accepted 6 September 2021

Published 24 August 2022