Combinatorial Characterizations and Branched Manifolds
Geometric Topology
2025-10-09 v1 Combinatorics
Abstract
A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the existence of a compact branched n-manifold W, such that the family is precisely those manifolds that immerse into W. In subsequent papers, the equivalence will be used to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD.
Keywords
Cite
@article{arxiv.2510.06514,
title = {Combinatorial Characterizations and Branched Manifolds},
author = {Daryl Cooper and Leslie Mavrakis and Priyam Patel},
journal= {arXiv preprint arXiv:2510.06514},
year = {2025}
}
Comments
13 pages, 2 figures