Rational homotopy of circle actions

Volker Hauschild

Vol. 191 (1999), No. 2, 275–311

DOI: 10.2140/pjm.1999.191.275

Abstract

We classify circle actions on F-spaces X with H^od(X; ℚ) = 0 up to equivariant rational homotopy equivalence by the concept of g-points in the spectrum of the cohomology ring of Baut₀(X). In the case of circle actions on closed oriented manifolds X with the rational cohomology of flag varieties K∕T this gives a generalization of the rational homotopy classification of linear (or homomorphic) circle actions to nonlinear S¹-actions.

Milestones

Received: 1 March 1998

Revised: 9 November 1998

Published: 1 December 1999