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Topological aspects of the projective unitary group

Mathematical Proceedings of the Cambridge Philosophical Society, 1970
1. Introduction. The group U(H) of unitary transformations of a complex Hilbert space H, endowed with its strong operator topology, is of interest in the study of unitary representations of a topological group. The unitary transformations of H induce a group U(Ĥ) of transformations of the associated projective space Ĥ. The projective unitary group U(Ĥ)
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[98] Topological Aspects of Loop Groups

2017
The purpose of these lectures is to give an introduction to the topological aspect s of the loop space ΩG when G is a compact Lie group. We will give a direct method of computing the cohomology of ΩG from very geometric and group theoretic data, usually referred to as the diagram.
László Fehér   +2 more
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Chemical applications of topology and group theory 27. Topological aspects of polyoxovanadate macropolyhedra

Journal of Molecular Structure: THEOCHEM, 1995
Abstract The square pyramidal VOtO4b and octahedral VOtO4bOi vertices of polyoxovanadates have non-bonding dxy orbitals, which can overlap weakly, leading to stabilization of derivatives with d1 VIV vertices through binodal orbital aromaticity. The S4 symmetry of dxy orbitals favors structures based on vanadium macropolyhedra with VOV edges and C4 ...
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Topological Aspects of the Theory of Group Actions

1985
In this chapter M denotes a C ∞ differentiable manifold and G a simply connected Lie group.
César Camacho, Alcides Lins Neto
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Closed-shell three-connected clusters: topological and group-theoretical aspects

Journal of the Chemical Society, Faraday Transactions, 1991
Group-theoretical and topological arguments are presented within the tensor surface harmonic framework in order to predict polyhedral geometries for three-connected pseudo-spherical clusters, such as the C2n fullerenes. Topological and symmetry relationships between polyhedra, their duals, edge-figures and truncated derivatives are outlined.
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Combinatorial Curvatures, Group Actions, and Colourings: Aspects of Topological Combinatorics

2005
The first part asks whether classical notions of curvature known from differential geometry can be carried over to discrete structures. Of particular interest are analogies on a structural level; questions of convergence are not considered. Chapter 1 is motivated by constructions well-known in differential geometry.
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