Crystallographic Topology 2: Overview And Work In Progress (1999)
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@MISC{Chemical99crystallographictopology,
author = {Carroll Johnson Chemical and Carroll K. Johnson},
title = {Crystallographic Topology 2: Overview And Work In Progress},
year = {1999}
}
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Abstract
This overview describes an application of contemporary geometric topology and stochastic process concepts to structural crystallography. In this application, crystallographic groups become orbifolds, crystal structures become Morse functions on orbifolds, and vibrating atoms in a crystal become vector valued Gaussian measures with the Radon-Nikodym property. Intended crystallographic benefits include new methods for visualization of space groups and crystal structures, analysis of the thermal motion patterns seen in ORTEP drawings, and a classification scheme for crystal structures based on their Heegaard splitting properties. 1 Introduction Geometric topology and structural crystallography concepts are combined to define a research area we call Structural Crystallographic Topology, or just Crystallographic Topology. The first paper in the series[30] describes basic crystallography concepts (crystallographic groups, lattice complexes, and crystal structures) and their replacement topo...
