Smooth gluing of group actions and applications
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- by Kiran Parkhe
- Proc. Amer. Math. Soc. 143 (2015), 203-212
- DOI: https://doi.org/10.1090/S0002-9939-2014-12231-3
- Published electronically: August 22, 2014
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Abstract:
Let $M_1$ and $M_2$ be two $n$-dimensional smooth manifolds with boundary. Suppose we glue $M_1$ and $M_2$ along some boundary components (which are, therefore, diffeomorphic). Call the result $N.$ If we have a group $G$ acting continuously on $M_1,$ and also acting continuously on $M_2,$ such that the actions are compatible on glued boundary components, then we get a continuous action of $G$ on $N$ that stitches the two actions together. However, even if the actions on $M_1$ and $M_2$ are smooth, the action on $N$ probably will not be smooth.
We give a systematic way of smoothing out the glued $G$-action. This allows us to construct interesting new examples of smooth group actions on surfaces and to extend a result of Franks and Handel (2006) on distortion elements in diffeomorphism groups of closed surfaces to the case of surfaces with boundary.
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Bibliographic Information
- Kiran Parkhe
- Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel
- Email: kiranparkhe2012@u.northwestern.edu
- Received by editor(s): October 30, 2012
- Received by editor(s) in revised form: March 14, 2013
- Published electronically: August 22, 2014
- Communicated by: Nimish Shah
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 203-212
- MSC (2010): Primary 37C85; Secondary 57M60, 37C05
- DOI: https://doi.org/10.1090/S0002-9939-2014-12231-3
- MathSciNet review: 3272745