Abstract
We show here that an infinite sequence of homotopy $4$-spheres constructed by Cappell-Shaneson are all diffeomorphic to $S^4$. This generalizes previous results of Akbulut-Kirby and Gompf.
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[a1]
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@article {a1, MRKEY = {1689337},
AUTHOR = {Akbulut, Selman},
TITLE = {Scharlemann's manifold is standard},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {149},
YEAR = {1999},
NUMBER = {2},
PAGES = {497--510},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {57N13 (57N70 57Q15 57Q25)},
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} -
[a2]
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@incollection {ar, MRKEY = {780575},
AUTHOR = {Aitchison, I. R. and Rubinstein, J. H.},
TITLE = {Fibered knots and involutions on homotopy spheres},
BOOKTITLE = {Four-Manifold Theory},
VENUE={{D}urham, {N}.{H}., 1982},
SERIES = {Contemp. Math.},
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[ak1]
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[ak2]
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[cs]
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[g1]
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author={Freedman, M. and Gompf, Robert E. and Morrison, S. and Walker, K.},
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[k]
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ZBLNUMBER = {0377.55001},
}