## Osaka Journal of Mathematics

### Self-bumpings on Kleinian once-punctured torus groups

Jiming Ma

#### Abstract

We give a new proof of the characterization of self-bumping points on the space of Kleinian once-punctured torus groups of Ito [8], based on some recent work of Bromberg [4].

#### Article information

Source
Osaka J. Math., Volume 51, Number 3 (2014), 823-829.

Dates
First available in Project Euclid: 23 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1414090804

Mathematical Reviews number (MathSciNet)
MR3272618

Zentralblatt MATH identifier
1302.57037

#### Citation

Ma, Jiming. Self-bumpings on Kleinian once-punctured torus groups. Osaka J. Math. 51 (2014), no. 3, 823--829. https://projecteuclid.org/euclid.ojm/1414090804

#### References

• J.W. Anderson and R.D. Canary: Cores of hyperbolic $3$-manifolds and limits of Kleinian groups, Amer. J. Math. 118 (1996), 745–779.
• J.W. Anderson and R.D. Canary: Algebraic limits of Kleinian groups which rearrange the pages of a book, Invent. Math. 126 (1996), 205–214.
• J.F. Brock, K.W. Bromberg, R.D. Canary and Y.N. Minsky: Local topology in deformation spaces of hyperbolic 3-manifolds, Geom. Topol. 15 (2011), 1169–1224.
• K. Bromberg: The space of Kleinian punctured torus groups is not locally connected, Duke Math. J. 156 (2011), 387–427.
• K. Bromberg and J. Holt: Self-bumping of deformation spaces of hyperbolic 3-manifolds, J. Differential Geom. 57 (2001), 47–65.
• R.D. Canary: Introductory bumponomics: the topology of deformation spaces of hyperbolic 3-manifolds; in Teichmüller Theory and Moduli Problem, Ramanujan Math. Soc., Mysore, 2010, 131–150.
• J. Holt and J. Souto: On the topology of the space of punctured torus, preprint (2006).
• K. Ito: Convergence and divergence of Kleinian punctured torus groups, Amer. J. Math. 134 (2012), 861–889.
• A.D. Magid: Deformation spaces of Kleinian surface groups are not locally connected, Geom. Topol. 16 (2012), 1247–1320.
• A. Marden: Outer circles–-An Introduction to Hyperbolic 3-Manifolds, Cambridge Univ. Press, Cambridge, 2007.
• H.A. Masur and Y.N. Minsky: Geometry of the complex of curves. II. Hierarchical structure, Geom. Funct. Anal. 10 (2000), 902–974.
• C.T. McMullen: Complex earthquakes and Teichmüller theory, J. Amer. Math. Soc. 11 (1998), 283–320.
• Y.N. Minsky: The classification of punctured-torus groups, Ann. of Math. (2) 149 (1999), 559–626.
• K. Ohshika: Divergence, exotic convergence and self-bumping in quasi-Fuchsian spaces, arXiv: math.GT/1010.0070 (2010).
• D.J. Wright: The shape of the boundary of the Teichmüller space of once-punctured tori in Maskit's embedding, preprint (1987).