How tightly can you fold a sphere? |
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Authors: | Jill McGowan |
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Institution: | a Howard University, Department of Mathematics, Washington DC, 20059, USA b Instituto de Matemáticas - UNAM, Cuernavaca, Apdo. Postal 273-3 Admon. 3, Cuernavaca, 62210, Mexico |
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Abstract: | Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. The quotient of Sn by this group action, Sn/G, has a natural metric on it, and so we may ask what are its diameter and q-extents. These values have been computed for cohomogeneity one actions on spheres. In this paper, we compute the diameters, extents, and several q-extents of cohomogeneity two orbit spaces resulting from such actions, and we also obtain results about the q-extents of Euclidean disks. Additionally, via a simple geometric criterion, we can identify which of these actions give rise to a decomposition of the sphere as a union of disk bundles. In addition, as a service to the reader, we give a complete breakdown of all the isotropy subgroups resulting from cohomogeneity one and two actions. |
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Keywords: | 53C10 57S25 22E45 |
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