Constructing Simplicial Branched Covers
Combinatorics
2008-01-23 v2 Geometric Topology
Abstract
Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d<=4. On the other hand, Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d<=4 every closed oriented PL d-manifold is the partial unfolding of some polytopal d-sphere.
Cite
@article{arxiv.0707.1411,
title = {Constructing Simplicial Branched Covers},
author = {Nikolaus Witte},
journal= {arXiv preprint arXiv:0707.1411},
year = {2008}
}
Comments
15 pages, 8 figures, typos corrected and conjecture added