Volume 14, issue 2 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 2, 549–862
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Quasisymmetric nonparametrization and spaces associated with the Whitehead continuum

Juha Heinonen and Jang-Mei Wu

Geometry & Topology 14 (2010) 773–798
Bibliography
1 L Ahlfors, A Beurling, Conformal invariants and function-theoretic null-sets, Acta Math. 83 (1950) 101 MR0036841
2 F D Ancel, J W Cannon, The locally flat approximation of cell-like embedding relations, Ann. of Math. $(2)$ 109 (1979) 61 MR519353
3 J J Andrews, L Rubin, Some spaces whose product with $E^{1}$ is $E^{4}$, Bull. Amer. Math. Soc. 71 (1965) 675 MR0176454
4 R H Bing, The cartesian product of a certain nonmanifold and a line is $E^{4}$, Ann. of Math. $(2)$ 70 (1959) 399 MR0107228
5 R H Bing, A set is a $3$ cell if its cartesian product with an arc is a $4$ cell, Proc. Amer. Math. Soc. 12 (1961) 13 MR0123303
6 M Bonk, B Kleiner, Quasisymmetric parametrizations of two-dimensional metric spheres, Invent. Math. 150 (2002) 127 MR1930885
7 J W Cannon, The recognition problem: what is a topological manifold?, Bull. Amer. Math. Soc. 84 (1978) 832 MR0494113
8 A V Černavskiĭ, Piece-wise linear approximation of embeddings of manifolds in codimensions greater than two. A supplement to the article “Piece-wise linear approximation of embeddings of cells and spheres in codimensions greater than two”, Mat. Sb. $($N.S.$)$ 82 (124) (1970) 499 MR0275438
9 R J Daverman, Decompositions of manifolds, Pure and Applied Math. 124, Academic Press (1986) MR872468
10 G David, S Semmes, Quantitative rectifiability and Lipschitz mappings, Trans. Amer. Math. Soc. 337 (1993) 855 MR1132876
11 R D Edwards, Suspensions of homology spheres arXiv:math/0610573
12 R D Edwards, The topology of manifolds and cell-like maps, from: "Proceedings of the International Congress of Mathematicians (Helsinki, 1978)", Acad. Sci. Fennica (1980) 111 MR562601
13 H Federer, Geometric measure theory, Grund. der math. Wissenschaften 153, Springer (1969) MR0257325
14 M H Freedman, R Skora, Strange actions of groups on spheres, J. Differential Geom. 25 (1987) 75 MR873456
15 B Fuglede, Extremal length and functional completion, Acta Math. 98 (1957) 171 MR0097720
16 F W Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962) 353 MR0139735
17 F W Gehring, The $L^{p}$–integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973) 265 MR0402038
18 J Heinonen, P Koskela, Definitions of quasiconformality, Invent. Math. 120 (1995) 61 MR1323982
19 J Heinonen, P Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998) 1 MR1654771
20 J Heinonen, S Semmes, Thirty-three yes or no questions about mappings, measures, and metrics, Conform. Geom. Dyn. 1 (1997) 1 MR1452413
21 R C Kirby, The topology of $4$–manifolds, Lecture Notes in Math. 1374, Springer (1989) MR1001966
22 T J Laakso, Plane with $A_\infty$–weighted metric not bi-Lipschitz embeddable to $\mathbb{R}^N$, Bull. London Math. Soc. 34 (2002) 667 MR1924353
23 O Martio, S Rickman, J Väisälä, Topological and metric properties of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I (1971) 31 MR0299782
24 R T Miller, Approximating codimension $3$ embeddings, Ann. of Math. $(2)$ 95 (1972) 406 MR0307246
25 E E Moise, Geometric topology in dimensions $2$ and $3$, Graduate Texts in Math. 47, Springer (1977) MR0488059
26 S Rickman, Quasiregular mappings, Ergebnisse der Math. und ihrer Grenzgebiete (3) 26, Springer (1993) MR1238941
27 C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, Springer Study Edition (1982) MR665919
28 T B Rushing, Topological embeddings, Pure and Applied Math. 52, Academic Press (1973) MR0348752
29 S Semmes, Chord-arc surfaces with small constant. II. Good parameterizations, Adv. Math. 88 (1991) 170 MR1120612
30 S Semmes, Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities, Selecta Math. $($N.S.$)$ 2 (1996) 155 MR1414889
31 S Semmes, Good metric spaces without good parameterizations, Rev. Mat. Iberoamericana 12 (1996) 187 MR1387590
32 S Semmes, On the nonexistence of bi-Lipschitz parameterizations and geometric problems about $A_\infty$–weights, Rev. Mat. Iberoamericana 12 (1996) 337 MR1402671
33 S Semmes, Some topics concerning homeomorphic parameterizations, Publ. Mat. 45 (2001) 3 MR1829576
34 L Siebenmann, D Sullivan, On complexes that are Lipschitz manifolds, from: "Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977)" (editor J C Cantrell), Academic Press (1979) 503 MR537747
35 P Tukia, J Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980) 97 MR595180
36 J Väisälä, Lectures on $n$–dimensional quasiconformal mappings, Lecture Notes in Math. 229, Springer (1971) MR0454009
37 G A Venema, Approximating disks in $4$–space, Michigan Math. J. 25 (1978) 19 MR497879
38 G A Venema, Approximating codimension two embeddings of cells, Pacific J. Math. 126 (1987) 165 MR868611
39 J H C Whitehead, A certain open manifold whose group is unity, Quart. J. Math. Oxford $(2)$ 6 (1935) 268
40 E C Zeeman, Unknotting spheres, Ann. of Math. $(2)$ 72 (1960) 350 MR0117738