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

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

2011-12-22

arxiv.org/abs/1112.5374v1

Mathematics

Geometric Topology

14 pages, 5 figures

Scientific paper

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).

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