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Equilibrium triangulations of the complex projective plane

✍ Scribed by T. F. Banchoff; W. Kühnel

Publisher
Springer
Year
1992
Tongue
English
Weight
905 KB
Volume
44
Category
Article
ISSN
0046-5755

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✦ Synopsis

Starting with the well-known 7-vertex triangulation of the ordinary torus, we construct a 10-vertex triangulation of CP 2 which fits the equilibrium decomposition of CP 2 in the simplest possible way. By suitable positioning of the vertices, the full automorphism group of order 42 is realized by a discrete group of isometries in the Fubini-Study metric. A slight subdivision leads to an elementary proof of the theorem of Kuiper-Massey which says that CP 2 modulo conjugation is PL homeomorphic to the standard 4-sphere. The branch locus of this identification is a 7-vertex triangulation RP72 of the real projective plane. We also determine all tight simplicial embeddings of Cp2o and RP 2.

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