Vol. 76, No. 1, 1978

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Tangent frame fields on spin manifolds

Duane Randall

Vol. 76 (1978), No. 1, 157–167
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 wn4M = 0 and w4M wn5M = 0. Then Mn admits a tangent 4-frame field iff

wn −3M = 0  and  χ2M  = 0.

Mathematical Subject Classification
Primary: 57D25, 57D25
Milestones
Received: 1 August 1977
Published: 1 May 1978
Authors
Duane Randall
Department of Mathematics and Computer Science
Loyola University
New Orleans LA 70118
United States