Search results for "Topological transformation"
showing 2 items of 2 documents
Three-dimensional topological loops with nilpotent multiplication groups
2015
In this paper we describe the structure of indecomposable nilpotent Lie groups which are multiplication groups of three-dimensional simply connected topological loops. In contrast to the 2-dimensional loops there is no connected topological loop of dimension ≥ 3 such that the Lie algebra of its multiplication group is an elementary filiform Lie algebra. We determine the indecomposable nilpotent Lie groups of dimension ≤ 6 and their subgroups which are the multiplication groups and the inner mapping groups of the investigated loops. We prove that all multiplication groups have 1-dimensional centre and the corresponding loops are centrally nilpotent of class 2.
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…