منابع مشابه
Isotopy Convergence Theorem
When approximating a space curve, it is natural to consider whether the knot type of the original curve is preserved in the approximant. This preservation is of strong contemporary interest in computer graphics and visualization. We establish a criterion to preserve knot type under approximation that relies upon convergence in both distance and total curvature.
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It is shown that many of the algebras arising in nonselective genetics are isotopes of the algebras for particularly simple systems of inheritance. Moreover, interesting aspects of the structure are preserved under the relevant isotopies.
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We investigate the following problem: Given two embeddings G1 and G2 of the same abstract graph G on an orientable surface S, decide whether G1 and G2 are isotopic; in other words, whether there exists a continuous family of embeddings between G1 and G2. We provide efficient algorithms to solve this problem in two models. In the first model, the input consists of the arrangement of G1 (resp., G...
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Four mutually dependent facts are proven. • A smooth saddle sphere in S has at least four inflection arches. • Each hyperbolic hérisson H generates an arrangement of disjoint oriented great semicircles on the unit sphere S. On the one hand, the semicircles correspond to the horns of the hérisson. On the other hand, they correspond to the inflection arches of the graph of the support function hH...
متن کاملLegendrian Mirrors and Legendrian Isotopy
We resolve a question of Fuchs and Tabachnikov by showing that there is a Legendrian knot in standard contact R with zero Maslov number which is not Legendrian isotopic to its mirror. The proof uses the differential graded algebras of Chekanov. A Legendrian knot in standard contact R is a knot which is everywhere tangent to the two-plane distribution induced by the contact one-form dz− y dx. Tw...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0524321-6