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Bulletin of the London Mathematical Society 2001 33(1):89-99; doi:10.1112/blms/33.1.89
© 2001 by London Mathematical Society
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© London Mathematical Society

The S1-Equivariant Cohomology of Homogeneous Spaces as Deformations of Algebras

Katsuhiko Kuribayashi

Department of Applied Mathematics, Okayama University of Science 700-0005 Okayama, Japan

Received 15 May 1999. Revision received 24 February 2000.

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; Fp) 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.

Current address: Université d'Angers Unité Algèbre et Géométrie, Boulevard Lavoisier, 49045 Angers, France; e-mail: kuri{at}geom.xmath.ous.ac.jp


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