Search results for "Writhe"

showing 2 items of 2 documents

Conformal invariance of the writhe of a knot

2008

We give a new proof of an old theorem by Banchoff and White 1975 that claims that the writhe of a knot is conformally invariant.

Mathematics - Differential GeometryPure mathematicsQuantitative Biology::BiomoleculesAlgebra and Number TheoryConformal mapGeometric Topology (math.GT)Mathematics::Geometric TopologyMathematics - Geometric TopologyDifferential Geometry (math.DG)Conformal symmetryFOS: Mathematics57M25 53A30Knot (mathematics)MathematicsWrithe
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Design and synthesis of the first triply twisted Möbius annulene.

2014

As long as 50 years ago theoretical calculations predicted that Mobius annulenes with only one π surface and one edge would exhibit peculiar electronic properties and violate the Huckel rules. Numerous synthetic attempts notwithstanding, the first singly twisted Mobius annulene was not prepared until 2003. Here we present a general, rational strategy to synthesize triply or even more highly twisted cyclic π systems. We apply this strategy to the preparation of a triply twisted [24]dehydroannulene, the structure of which was confirmed by X-ray analysis. Our strategy is based on the topological transformation of 'twist' into 'writhe'. The advantage is twofold: the product exhibits a lower deg…

Surface (mathematics)Models MolecularMacrocyclic CompoundsMolecular StructureChemistryGeneral Chemical EngineeringStructure (category theory)Molecular ConformationGeneral ChemistryAnnuleneTopological transformationTheoretical physicsComputational chemistryProduct (mathematics)TwistLower degreeWritheNature chemistry
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