Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Inertial and bordism properties of spheres


Author: Allan Brender
Journal: Proc. Amer. Math. Soc. 27 (1971), 209-212
MSC: Primary 57.10
MathSciNet review: 0267592
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Abstract: The $ k$-connective bounding group $ {\theta ^n}(k)$ and the $ k$-connective inertial group $ {I^n}(k)$ are defined as subgroups of $ {\theta ^n}$, the group of smooth $ n$-spheres, $ n \geqq 7$. It is shown $ {I^n}(k)$ is contained in $ {\theta ^n}(k)$. Consequently, the image of the Milnor-Novikov pairing $ {\tau _{n,k}}$ is contained in $ {\theta ^{n + k}}(k)$ when $ n \geqq k + 2$. It follows that $ {\tau _{7,3}} = 0$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0267592-9
Keywords: $ k$-connective cobordism, inertia group, exotic spheres
Article copyright: © Copyright 1971 American Mathematical Society