Vol. 53, No. 2, 1974

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On conjugation cobordism

Duane O’Neill

Vol. 53 (1974), No. 2, 573–577

An almost-complex manifold supports an involution if there is a differentiable self-map on the manifold of period two. The differential of the map acts on the coset space of the almost-complex structures on M by inner automorphism. This action is also of period two. If the almost-complex structure is sent to its conjugate, the manifold with structure, together with the given involution is called a conjugation. Any linear involution of Euclidean space may be used to stabilize this situation, giving a cobordism theory of exotic conjugations. The question considered here is: What is the image in complex cobordism of the functor which forgets equivariance. The result shown in the next section is: If a stably almost-complex manifold supports an exotic conjugation, every characteristic number is even.

Mathematical Subject Classification
Primary: 57D85
Received: 19 September 1973
Published: 1 August 1974
Duane O’Neill