TL;DR
This paper proves that any smooth manifold can be smoothly triangulated in a way that is transverse to a specified smooth map, removing a key assumption used in previous constructions.
Contribution
It establishes the existence of transverse smooth triangulations for all smooth manifolds without requiring the map to be proper, advancing the theory of manifold triangulations.
Findings
Every smooth manifold admits a smooth triangulation transverse to a given smooth map.
Removes the properness assumption in Scharlemann's construction.
Enhances understanding of manifold triangulations in differential topology.
Abstract
We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann's construction [5].
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis