Topologically chiral object

An object, such as a knot, or a link, or a graph, is topologically chiral if and only if it cannot be converted into its mirror image by continuous deformation (ambient isotopy) in the object s space otherwise it is topologically achiral. 

In numerous cases, it may be useful to realize that all these chiral structures may be described in terms of helicity [47], that is the arrangement of atoms can be described as a combined rotation and translation. If all the compounds presented above require a certain rigidity to be chiral, there are however molecules which do not require any rigidity at all to remain chiral. This seems at first paradoxical, but it is the case of the so-called topologically chiral molecules (as opposed to Euclidean chiral molecules). Before examining these objects, it is necessary to briefly review the bases of molecular topology. 

Experimental data about the properties of Mobius strip-like structures as the ladder 129a or knots like 127 are rather scarce. However, a theoretical analysis of the peculiarities of these constructions (see refs. 18a-d, 21b, 21c and literature cited therein) led to some conclusions of general importance. Thus it was established that a new phenomenon of topological chirality should be observed for compounds having the shape of trefoil knots or Mobius strips. Normally, chemists deal with chiral objects which can be (in principle) transformed into their mirror image by a continuous deformation. For... 

Certain types of knots and links exist as topologically chiral enan-tiomorphs. Such enantiomorphs cannot be interconverted by continuous deformation ( ambient isotopy ). Homochirality classes can therefore be defined for this type of mathematical object. ... 

The major obstacles presented by the overall objective to create carbon-carbon bonds asymmetrically via chiral enolates are therefold in nature Given the carbonyl derivative (163), the chiral auxiliary moiety A must provide a strong bias for a highly selective enolization process A it must also provide a strong topological bias for... 

After the sol-gel process, the preformed helical silica network has embedded probably enough chiral information to be amplified (reinforced) irreversibly during the calcination process when almost total condensation of Si-OH bonds occurs. By calcinations of the hybrid material, the templating twisted G-quadruplex architectures are eliminated, and inorganic silica anisotropic microsprings are obtained. They present the same helical topology, without inversion inside the helix. These objects have a different helical pitch, which depends strongly on... 

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