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A remark on the genus of the infinite quaternionic projective space

Elsevier B.V.
Publication Date
  • Geometry And Topology
  • Pure_Mathematics/0107007
  • Mathematics


It is shown that only countably many spaces in the genus of hp ∞, the infinite quaternionic projective space, can admit essential maps from cp ∞, the infinite complex projective space. Examples of countably many homotopically distinct spaces in the genus of hp ∞ which admit essential maps from cp ∞ are constructed. These results strengthen a theorem of McGibbon and Rector which states that among the uncountably many homotopy types in its genus, hp ∞ is the only one which admits a maximal torus.

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