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Classification of Nash manifolds

Masahiro Shiota (1983)

Annales de l'institut Fourier

A semi-algebraic analytic manifold and a semi-algebraic analytic map are called a Nash manifold and a Nash map respectively. We clarify the category of Nash manifolds and Nash maps.

Classifying finite-sheeted covering mappings of paracompact spaces.

Vlasta Matijevic (2003)

Revista Matemática Complutense

The main result of the present paper is a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. This theorem is a generalization of the classical classification theorem for covering mappings over a connected locally pathwise connected semi-locally 1-connected space in the finite-sheeted case. To achieve the result we use the classification theorem for overlay structures which was recently proved by S. Mardesic and V. Matijevic (Theorems 1 and 4 of [5]).

Classifying toposes and foliations

Ieke Moerdijk (1991)

Annales de l'institut Fourier

For any etale topological groupoid G (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space B Γ q .

Clifford algebra with Reduce

Brackx, Freddy, Constales, Denis, Delanghe, Richard, Serras, Herman (1987)

Proceedings of the Winter School "Geometry and Physics"

Climbing a Legendrian mountain range without stabilization

Douglas J. LaFountain, William W. Menasco (2014)

Banach Center Publications

We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specific Legendrian and transversal MTWS by enhancing the Legendrian mountain range for the (2,3)-cable of a (2,3)-torus knot provided by Etnyre and Honda, and showing that elementary negative...

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