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Triangulations of Surfaces with Boundary and the Homotopy Principle for Functions without Critical Points

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Abstract

We consider triangulations of surfaces with boundary and marked points. These triangulations are classified with respect to flip equivalence. The results obtained are applied to the homotopy classification of functions without critical points on 2-manifolds. It is shown that the set of such functions satisfies the one-parametric h-principle.

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  1. Mathematics College, Independent University of Moscow, 11, Bolshoy Vlasievskiy Pereulok, Moscow, Russia

    Yu. M. Burman

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  1. Yu. M. Burman
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Burman, Y.M. Triangulations of Surfaces with Boundary and the Homotopy Principle for Functions without Critical Points. Annals of Global Analysis and Geometry 17, 221–238 (1999). https://doi.org/10.1023/A:1006556632099

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  • DOI: https://doi.org/10.1023/A:1006556632099

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