Singular vertices of nonnegatively curved integral polyhedral 3-manifolds

TL;DR

This paper classifies all possible types of highly singular points in nonnegatively curved 3-dimensional polyhedral manifolds with integral monodromy, establishing bounds on their quantity.

Contribution

It provides a complete classification of 32 singularity types and proves a bound on their number in such manifolds, advancing understanding of their geometric structure.

Findings

32 isometry types of singularities classified

Bound established on the number of singularities

Insights into the structure of nonnegatively curved polyhedral 3-manifolds

Abstract

In this paper, we study polyhedral 3-manifolds with nonnegative curvature and integral monodromy, two conditions motivated by Thurston's work in arXiv:math/9801088. We classify the 32 isometry types of codimension 3 singularities in such manifolds. We also show that the number of these singularities is bounded.