A bilinear form for Spin manifolds

Landweber, Peter S.; Stong, Robert E.

doi:10.1090/S0002-9947-1987-0876469-3

A bilinear form for Spin manifolds
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by Peter S. Landweber and Robert E. Stong PDF

Trans. Amer. Math. Soc. 300 (1987), 625-640 Request permission

Abstract:

This paper studies the bilinear form on ${H^j}(M;{Z_2})$ defined by $\left [ {x, y} \right ] = x {\text {S}}{{\text {q}}^2}y[M]$ when $M$ is a closed Spin manifold of dimension $2j + 2$. In analogy with the work of Lusztig, Milnor, and Peterson for oriented manifolds, the rank of this form on integral classes gives rise to a cobordism invariant.

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