Combinatorial Characterizations and Branched Manifolds

Fuente: arXiv
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Main Authors: Cooper, Daryl, Mavrakis, Leslie, Patel, Priyam
Format: Preprint
Published: 2025
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author Cooper, Daryl
Mavrakis, Leslie
Patel, Priyam
author_facet Cooper, Daryl
Mavrakis, Leslie
Patel, Priyam
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_06514
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Combinatorial Characterizations and Branched Manifolds
Cooper, Daryl
Mavrakis, Leslie
Patel, Priyam
Geometric Topology
Combinatorics
57Q99
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.
title Combinatorial Characterizations and Branched Manifolds
topic Geometric Topology
Combinatorics
57Q99
url https://arxiv.org/abs/2510.06514