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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the action of $ \Theta \sp{n}$. I


Author: H. E. Winkelnkemper
Journal: Trans. Amer. Math. Soc. 206 (1975), 339-346
MSC: Primary 57D60
DOI: https://doi.org/10.1090/S0002-9947-1975-0413136-6
MathSciNet review: 0413136
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Abstract: We prove two theorems about the inertia groups of closed, smooth, simply-connected $ n$-manifolds. Theorem A shows that, in certain dimensions, the special inertia group, unlike the full inertia group, can never be equal to $ {\Theta ^n}$; Theorem B shows, in $ \operatorname{dimensions} \equiv 3\bmod 4$, how to construct explicit closed $ n$-manifolds $ {M^n}$ such that $ \Theta (\partial \pi )$ is contained in the inertia group of $ {M^n}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0413136-6
Keywords: Homotopy sphere, inertia group, $ h$-cobordism, first exotic class
Article copyright: © Copyright 1975 American Mathematical Society