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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Smoothability of $ \mathbb{Z}\times\mathbb{Z}$-actions on 4-manifolds


Author: Nobuhiro Nakamura
Journal: Proc. Amer. Math. Soc. 138 (2010), 2973-2978
MSC (2010): Primary 57S05; Secondary 57M60, 57R57
Published electronically: March 23, 2010
MathSciNet review: 2644908
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Abstract: We construct a nonsmoothable $ \mathbb{Z}\times\mathbb{Z}$-action on the connected sum of an Enriques surface and $ S^2\times S^2$, such that each of the generators is smoothable. We also construct a nonsmoothable self-homeomorphism on an Enriques surface.


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Additional Information

Nobuhiro Nakamura
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Email: nobuhiro@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10413-4
PII: S 0002-9939(10)10413-4
Keywords: Group action, smoothability, Enriques surface
Received by editor(s): February 23, 2009
Received by editor(s) in revised form: November 22, 2009
Published electronically: March 23, 2010
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society