Geometry & Topology Volume 11, issue 1 (2007)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk

David Epstein and Vladimir Markovic

Geometry & Topology 11 (2007) 517–595

DOI: 10.2140/gt.2007.11.517

Bibliography

1	L V Ahlfors, Lectures on quasiconformal mappings, Manuscript prepared with the assistance of C J Earle, Jr., Van Nostrand Mathematical Studies 10 (1966) MR0200442
2	A Beurling, L Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956) 125 MR0086869
3	A Casson, D Jungreis, Convergence groups and Seifert fibered $3$-manifolds, Invent. Math. 118 (1994) 441 MR1296353
4	A Douady, C J Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986) 23 MR857678
5	D B A Epstein, Functors between tensored categories, Invent. Math. 1 (1966) 221 MR0213412
6	D B A Epstein, A Marden, V Markovic, Quasiconformal homeomorphisms and the convex hull boundary, Ann. of Math. $(2)$ 159 (2004) 305 MR2052356
7	D B A Epstein, W P Thurston, Transformation groups and natural bundles, Proc. London Math. Soc. (3) 38 (1979) 219 MR531161
8	D Gabai, Convergence groups are Fuchsian groups, Ann. of Math. $(2)$ 136 (1992) 447 MR1189862
9	F P Gardiner, D P Sullivan, Symmetric structures on a closed curve, Amer. J. Math. 114 (1992) 683 MR1175689
10	É Ghys, Prolongements des difféomorphismes de la sphère, Enseign. Math. $(2)$ 37 (1991) 45 MR1115743
11	J A Giblin, On the structure of homeomorphism groups, PhD thesis, University of Warwick (2007)
12	A Hinkkanen, Abelian and nondiscrete convergence groups on the circle, Trans. Amer. Math. Soc. 318 (1990) 87 MR1000145
13	A Hinkkanen, The structure of certain quasisymmetric groups, Mem. Amer. Math. Soc. 83 (1990) MR948926
14	S P Kerckhoff, The Nielsen realization problem, Ann. of Math. $(2)$ 117 (1983) 235 MR690845
15	B Knaster, C Kuratowski, Sur les ensembles connexes, Fund. Math. 2 (1922) 206
16	V Markovic, Realization of the mapping class group by homeomorphisms
17	V Markovic, Quasisymmetric groups, J. Amer. Math. Soc. 19 (2006) 673 MR2220103
18	J N Mather, Integrability in codimension $1$, Comment. Math. Helv. 48 (1973) 195 MR0356085
19	S Morita, Geometry of characteristic classes, Translations of Mathematical Monographs 199, Amer. Math. Soc. (2001) MR1826571
20	J F Plante, Subgroups of continuous groups acting differentiably on the half-line, Ann. Inst. Fourier (Grenoble) 34 (1984) 47 MR743621
21	D Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, from: "Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (Stony Brook, 1978)", Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 465 MR624833
22	T Tsuboi, On the foliated products of class $C^1$, Ann. of Math. $(2)$ 130 (1989) 227 MR1014925
23	P Tukia, On two-dimensional quasiconformal groups, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980) 73 MR595178
24	P Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math. 391 (1988) 1 MR961162