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Proceedings of the American Mathematical Society

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

 

 

On the inertia groups of fibre bundles


Author: Michael Frame
Journal: Proc. Amer. Math. Soc. 85 (1982), 289-292
MSC: Primary 57R55; Secondary 57R22
DOI: https://doi.org/10.1090/S0002-9939-1982-0652460-8
MathSciNet review: 652460
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Abstract: A subgroup $ \tilde I(M \times {S^i})$ of the inertia group $ I(M \times {S^i})$ is defined and shown to lie in $ I(C)$ for every fibre bundle $ {M^n} \to C \to {N^i}$. For certain $ M$, examples of nontrivial elements in $ \tilde I(M \times {S^i})$ are constructed using the $ \tau $-pairing of Milnor-Munkres-Novikov. For compact mapping tori $ {M_g}$ it is shown that $ I({M_g}) = I(M \times {S^1})$ if $ {\pi _1}M$ is finite and $ {\text{Wh}}({\pi _1}M) = 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0652460-8
Keywords: Exotic sphere, inertia groups, fibre bundle, Whitehead group
Article copyright: © Copyright 1982 American Mathematical Society