Let M1 and M2 be two n-dimensional smooth manifolds with boundary. Suppose we glue M1 and M2 along some boundary components (which are, therefore, diffeomorphic). Call the result N. If we have a group G acting continuously on M1, and also acting continuously on M2, 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 M1 and M2 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.
|Original language||English (US)|
|Number of pages||10|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Jan 1 2015|
- Distortion element
- Group action
- Heisenberg group
- Manifold with boundary
ASJC Scopus subject areas
- Applied Mathematics