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Transactions of the American Mathematical Society

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

 
 

 

On the action of $\Theta ^{n}$. 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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Keywords: Homotopy sphere, inertia group, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$h$">-cobordism, first exotic class
Article copyright: © Copyright 1975 American Mathematical Society