Pin and Pin′ cobordism

Giambalvo, V.

doi:10.1090/S0002-9939-1973-0321123-5

Pin and Pin cobordism

Author: V. Giambalvo
Journal: Proc. Amer. Math. Soc. 39 (1973), 395-401
MSC: Primary 57D90
DOI: https://doi.org/10.1090/S0002-9939-1973-0321123-5
MathSciNet review: 0321123
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Abstract: The cobordism group $\Omega _ \ast ^{\operatorname{Pi} n'}$ of smooth manifolds with a Pin structure on the stable normal bundle is computed. The image $\Omega _ \ast ^{\operatorname{Pi} n'} \to {\mathfrak{N}_ \ast }$ is determined, and some generators for $\Omega _ \ast ^{\operatorname{Pin} }$ and $\Omega _ \ast ^{\operatorname{Pi} n'}$ are given.

[1] 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 219077, https://doi.org/10.2307/1970690
[2] D. W. Anderson, E. H. Brown Jr., and F. P. Peterson, Pin cobordism and related topics, Comment. Math. Helv. 44 (1969), 462–468. MR 261613, https://doi.org/10.1007/BF02564545
[3] M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), no. suppl, suppl. 1, 3–38. MR 167985, https://doi.org/10.1016/0040-9383(64)90003-5
[4] V. Giambalvo, Cobordism of line bundles with a relation, Illinois J. Math. 17 (1973), 442–449. MR 0321121
[5] H. R. Margolis, On the realizability of modules over the Steenrod algebra, Bull. Amer. Math. Soc. 78 (1972), 564–567. MR 310885, https://doi.org/10.1090/S0002-9904-1972-13002-7
[6] Robert E. Stong, Notes on cobordism theory, Mathematical notes, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0248858