Skip to main content

Preliminaries

  • Chapter
  • First Online:
  • 685 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2231))

Abstract

In this chapter, we briefly review well-known facts on circle actions and on (discrete or indiscrete) subgroups of \( \operatorname {\mathrm {PSL}}_2(\mathbb {R})\).

This is a preview of subscription content, log in via an institution.

Buying options

eBook
USD   14.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   19.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. A.F. Beardon, The Geometry of Discrete Groups, 1st edn. Graduate Texts in Mathematics, vol. 91 (Springer, New York, 1983)

    Book  Google Scholar 

  2. M. Bucher, R. Frigerio, T. Hartnick, A note on semi-conjugacy for circle actions. Enseign. Math. 62(3–4), 317–360 (2016). MR 3692890

    Article  MathSciNet  Google Scholar 

  3. D. Calegari, Foliations and the Geometry of 3-Manifolds. Oxford Mathematical Monographs (Oxford University Press, Oxford, 2007). MR 2327361 (2008k:57048)

    Google Scholar 

  4. D. Calegari, A. Walker, Ziggurats and rotation numbers. J. Mod. Dyn. 5(4), 711–746 (2011). MR 2903755

    Google Scholar 

  5. É. Ghys, Actions de réseaux sur le cercle. Invent. Math. 137(1), 199–231 (1999). MR 1703323 (2000j:22014)

    Article  MathSciNet  Google Scholar 

  6. É. Ghys, Groups acting on the circle. Enseign. Math. (2) 47(3–4), 329–407 (2001). MR 1876932 (2003a:37032)

    Google Scholar 

  7. M. Jankins, W.D. Neumann, Rotation numbers of products of circle homeomorphisms. Math. Ann. 271(3), 381–400 (1985). MR 787188

    Article  MathSciNet  Google Scholar 

  8. K. Mann, Rigidity and flexibility of group actions on the circle, in Handbook of Group Actions (2015, to appear)

    Google Scholar 

  9. K. Mann, Spaces of surface group representations. Invent. Math. 201(2), 669–710 (2015). MR 3370623

    Article  MathSciNet  Google Scholar 

  10. R. Naimi, Foliations transverse to fibers of Seifert manifolds. Comment. Math. Helv. 69(1), 155–162 (1994). MR 1259611

    Article  MathSciNet  Google Scholar 

  11. A. Navas, Groups of Circle Diffeomorphisms, Spanish edn. Chicago Lectures in Mathematics (University of Chicago Press, Chicago, 2011). MR 2809110

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kim, Sh., Koberda, T., Mj, M. (2019). Preliminaries. In: Flexibility of Group Actions on the Circle. Lecture Notes in Mathematics, vol 2231. Springer, Cham. https://doi.org/10.1007/978-3-030-02855-8_2

Download citation

Publish with us

Policies and ethics