Smooth gluing of group actions and applications

Kiran Parkhe*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)203-212
Number of pages10
JournalProceedings of the American Mathematical Society
Volume143
Issue number1
StatePublished - Jan 1 2015

Keywords

  • Distortion element
  • Gluing
  • Group action
  • Heisenberg group
  • Manifold with boundary
  • Smoothing

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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