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THE S1-EQUIVARIANT COHOMOLOGY OF HOMOGENEOUS SPACES AS DEFORMATIONS OF ALGEBRAS

Published online by Cambridge University Press:  18 April 2001

KATSUHIKO KURIBAYASHI
KATSUHIKO KURIBAYASHI
Affiliation:
Department of Applied Mathematics, Okayama University of Science, 700-0005 Okayama, Japan Current address: Université d'Angers Unité Algèbre et Géométrie, Boulevard Lavoisier, 49045 Angers, France; e-mail: [email protected]
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Abstract

Let G be a compact connected Lie group and K a maximal rank subgroup of G. The homogeneous space G/K has the S1-action defined by left translations induced from a homomorphism from S1 to G. In this paper, we study a problem on the realization of some deformation of the cohomology algebra H*(G/K; [ ]p) by the S1-equivariant cohomology of G/K. In consequence, for the case where G is a classical Lie group, it follows that there exists at most one essentially different homomorphism from S1 to G which realizes a given deformation, and that the homomorphism is controlled by an appropriate equation in one indeterminate.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 1 , January 2001 , pp. 89 - 99
Copyright
© The London Mathematical Society 2001

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