Triangulations of surfaces with boundary and the homotopy principle for functions without critical points
type: Item
instance of: scholarly article
title: Triangulations of surfaces with boundary and the homotopy principle for functions without critical points
zbMATH Open document ID: 0949.57013
DOI: 10.1023/A:1006556632099
author: Yu Burman
published in: Annals of Global Analysis and Geometry
publication date: 1999-11-11T00:00:00Z
review text: The author considers triangulations of compact surfaces with boundary and marked points. This is connected with the moduli space of Euclidean structures on the sphere with conical singularities, bifurcation diagrams of quadratic differentials, Teichmüller space and complexity of fiber bundles. Allowing that a vertex may belong to an edge or a face, a more general definition of triangulation is given. Basic transformations called flips are defined and it is shown that two triangulations are connected by means of a finite number of flips (flip equivalence). Later on, an additional structure, marked vertices, are added to triangulations and it is shown that the flip equivalence need not always be satisfied. After considering relations between some spaces and their connected components, and then defining homotopy equivalence between these spaces, the author associates a generic function to each triangulation. In that way homotopy classification of functions not having critical points is reduced to the description of triangulations with marked points up to homotopy and flips.
Mathematics Subject Classification ID: 57M99
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 58D27
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 1333261
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
full work available at URL: a:1006556632099
OpenAlex ID: W2588755668
description: scientific article; zbMATH DE number 1333261