Piecewise-linear pseudodiagrams
Geometric Topology
2013-09-04 v2
Abstract
There are 2^n possible resolutions of a smooth pseudodiagram with n precrossings. If we consider piecewise-linear (PL) pseudodiagrams and resolutions that themselves are PL, certain resolutions of the pseudodiagram may not exist in three-space. We investigate this situation and its impact on the weighted resolution set of PL pseudodiagrams as well as introduce a concept specific to PL pseudodiagrams, the forcing number. Our main result classifies the PL shadows whose weighted resolution sets differ from the weighted resolution set that would exist in the smooth case.
Cite
@article{arxiv.1308.6776,
title = {Piecewise-linear pseudodiagrams},
author = {Molly Durava and Neil R. Nicholson and Jackson Ramsey},
journal= {arXiv preprint arXiv:1308.6776},
year = {2013}
}
Comments
7 pages, 8 figures; V2 fixes a minor typo in both statement of Cor. 2.8 and in its proof