On stable parallelizability of flag manifolds

Parameswaran Sankaran and Peter Zvengrowski

Vol. 122 (1986), No. 2, 455–458

DOI: 10.2140/pjm.1986.122.455

Abstract

It was shown by Trew and Zvengrowski that the only Grassmann manifolds that are stably parallelizable as real manifolds are G₁(F²), G₁(R⁴)≅G₃(R⁴), and G₁(R⁸)≅G₇(R⁸) where F = R,C, or H, the case F = R having also been previously treated by several authors. In this paper we solve the more general question of stable parallelizability of F-flag manifolds, F = R,C, or H. Only elementary vector bundle concepts are used. The real case has also been recently solved by Korbaš using Stiefel-Whitney classes.

Mathematical Subject Classification 2000

Primary: 57R15

Milestones

Received: 24 January 1985

Published: 1 April 1986