Euler-Poincar\'e obstruction for pretzels with long tentacles \`a la Cantor-Nyikos
Geometric Topology
2011-12-23 v1 Dynamical Systems
Abstract
We present an avatar of the Euler obstruction to foliated structures on certain non-metric surfaces. This adumbrates (at least for the simplest 2D-configurations) that the standard mechanism---to the effect that the devil of algebra sometimes barricades the existence of angelic geometric structures (obstruction theory more-or-less)---propagates slightly beyond the usual metrical proviso. Alas, the game is much more conservative than revolutionary: in particular we enjoyed retrospecting at Poincar\'e's argument of 1885 (announced in 1881).
Keywords
Cite
@article{arxiv.1112.5374,
title = {Euler-Poincar\'e obstruction for pretzels with long tentacles \`a la Cantor-Nyikos},
author = {Alexandre Gabard},
journal= {arXiv preprint arXiv:1112.5374},
year = {2011}
}
Comments
14 pages, 5 figures