Euler-Poincaré obstruction for pretzels with long tentacles à la Cantor-Nyikos

Alexandre Gabard

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arXiv · 1112.5374

Euler-Poincaré obstruction for pretzels with long tentacles à la Cantor-Nyikos

Alexandre Gabard

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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).

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Alexandre Gabard. 2011-12-22. Euler-Poincaré obstruction for pretzels with long tentacles à la Cantor-Nyikos. https://arxiv.org/abs/1112.5374

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