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On a distance function between Differentiable structures*

Published online by Cambridge University Press:  22 January 2016

Yoshihiro Shikata
Yoshihiro Shikata*
Affiliation:
Nagoya University
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In this note, we investigate a relation between the connected sum of manifolds and the distance of manifolds ([2]). Since the smoothing of a piecewise linear equivalence is given by connected sum of exotic spheres ([1]), we have a certain estimate of the smoothing obstruction using the distance of manifolds (Proposition 3). In § 3, an application is given to show the impossibility of the 0.64-pinching of an exotic sphere.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 53 - 60
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Munkres, J.: Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math., Vol. 72 (1960) 521–554.Google Scholar
[2] Shikata, Y.: On a distance function on the set of differentiable structure, Osaka J. Math., Vol. 3 (1966) 293–301.Google Scholar
[3] Shikata, Y.: On Pontriagin classes, I, J. of Math. Osaka City Univ., Vol. 13 (1963) 73–86.Google Scholar
[4] Shikata, Y.: On the differentiable pinching problem, Osaka J. Math., Vol. 4 (1967) 279–287.Google Scholar