Euler-Poincaré obstruction for pretzels with long tentacles à la Cantor-Nyikos
arXiv:1112.5374
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 Poincaré's argument of 1885 (announced in 1881).
arXiv comment14 pages, 5 figures