Tangent frame fields on spin manifolds

Duane Randall

Vol. 76 (1978), No. 1, 157–167

DOI: 10.2140/pjm.1978.76.157

Abstract

In this note we prove the following theorems.

Theorem A. Let Mⁿ be a spin manifold with n ≡ 7 mod 8 and n > 7. Then M admits at least 8 nonhomotopic tangent 4-frame fields.

Theorem B. Let Mⁿ be a spin manifold with n ≡ 3 mod 8 and n > 3. Suppose that w_n−4M = 0 and w₄M ⋅ w_n−5M = 0. Then Mⁿ admits a tangent 4-frame field iff

Mathematical Subject Classification

Primary: 57D25, 57D25

Milestones

Received: 1 August 1977

Published: 1 May 1978