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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A bilinear form for Spin manifolds


Authors: Peter S. Landweber and Robert E. Stong
Journal: Trans. Amer. Math. Soc. 300 (1987), 625-640
MSC: Primary 57R20; Secondary 57R15, 57R90
MathSciNet review: 876469
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0876469-3
PII: S 0002-9947(1987)0876469-3
Article copyright: © Copyright 1987 American Mathematical Society