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Generating varieties for the triple loop space of classical Lie groups

Yasuhiko Kamiyama (2003)

Fundamenta Mathematicae

For G = SU(n), Sp(n) or Spin(n), let C G ( S U ( 2 ) ) be the centralizer of a certain SU(2) in G. We have a natural map J : G / C G ( S U ( 2 ) ) Ω ³ G . For a generator α of H ( G / C G ( S U ( 2 ) ) ; / 2 ) , we describe J⁎(α). In particular, it is proved that J : H ( G / C G ( S U ( 2 ) ) ; / 2 ) H ( Ω ³ G ; / 2 ) is injective.

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