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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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  • [ABP] D. W. Anderson, E. H. Brown, Jr., and F. P. Peterson, The structure of the Spin cobordism ring, Ann. of Math. (2) 86 (1967), 271-298. MR 0219077 (36:2160)
  • [B1] W. Browder, Remark on the Poincaré duality theorem, Proc. Amer. Math. Soc. (2) 13 (1962), 927-930. MR 0143205 (26:765)
  • [B2] W. Browder, Torsion in $ H$-spaces, Ann. of Math. (2) 74 (1961), 24-51. MR 0124891 (23:A2201)
  • [B3] E. H. Brown, Jr., Generalizations of the Kervaire invariant, Ann. of Math. (2) 95 (1972), 368-383. MR 0293642 (45:2719)
  • [F] E. E. Floyd, The number of cells in a nonbounding manifold, Ann. of Math. (2) 98 (1973), 210-225. MR 0334256 (48:12575)
  • [K] S. M. Kahn, Involutions on odd-dimensional manifolds and the de Rham invariant, Topology (to appear). MR 899050 (89c:57050)
  • [LMP] G. Lusztig, J. Milnor, and F. P. Peterson, Semicharacteristics and cobordism, Topology 8 (1969), 357-359. MR 0246308 (39:7612)
  • [S] R. E. Stong, Appendix: Calculation of $ \Omega _{11}^{{\operatorname{Spin}}}(K(Z,\,4))$, Unified String Theories, edited by M. Green and D. Gross, World Scientific Press, Singapore, 1986, pp. 430-437. MR 849112
  • [W] W. S. Wilson, A new relation on the Stiefel-Whitney classes of spin manifolds, Illinois J. Math. 17 (1973), 115-127. MR 0310883 (46:9981)

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Article copyright: © Copyright 1987 American Mathematical Society

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