The cohomology ring of the spaces of loops on Lie groups and homogeneous spaces

Katsuhiko Kuribayashi

Vol. 163 (1994), No. 2, 361–391

DOI: 10.2140/pjm.1994.163.361

Abstract

Let X be a simply connected space whose mod p cohomology is isomorphic to that of a compact, simply connected, simple Lie group as an algebra over the Steenrod algebra. We determine the algebra structure of the mod p cohomology of ΩX algebraically. Moreover we give a method to determine the algebra structure of the mod p cohomology of the space of loops on a homogeneous space.

Mathematical Subject Classification 2000

Primary: 55P35

Secondary: 57T10

Milestones

Received: 22 August 1991

Revised: 20 November 1991

Published: 1 April 1994