Volume 20, issue 5 (2016)

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
Surface group representations to $\mathrm{SL}(2,\mathbb{C})$ and Higgs bundles with smooth spectral data

Richard A Wentworth and Michael Wolf

Geometry & Topology 20 (2016) 3019–3032
Bibliography
1 F Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. 124 (1986) 71 MR847953
2 K Corlette, Flat G–bundles with canonical metrics, J. Differential Geom. 28 (1988) 361 MR965220
3 M Culler, J W Morgan, Group actions on R–trees, Proc. London Math. Soc. 55 (1987) 571 MR907233
4 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. 117 (1983) 109 MR683804
5 G Daskalopoulos, S Dostoglou, R Wentworth, On the Morgan–Shalen compactification of the SL(2,C) character varieties of surface groups, Duke Math. J. 101 (2000) 189 MR1738182
6 S K Donaldson, Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. 55 (1987) 127 MR887285
7 D Gallo, M Kapovich, A Marden, The monodromy groups of Schwarzian equations on closed Riemann surfaces, Ann. of Math. 151 (2000) 625 MR1765706
8 W M Goldman, R A Wentworth, Energy of twisted harmonic maps of Riemann surfaces, from: "In the tradition of Ahlfors–Bers, IV" (editors D Canary, J Gilman, J Heinonen, H Masur), Contemp. Math. 432, Amer. Math. Soc. (2007) 45 MR2342806
9 N J Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987) 59 MR887284
10 N Hitchin, Stable bundles and integrable systems, Duke Math. J. 54 (1987) 91 MR885778
11 J Hubbard, H Masur, Quadratic differentials and foliations, Acta Math. 142 (1979) 221 MR523212
12 J Jost, Equilibrium maps between metric spaces, Calc. Var. Partial Differential Equations 2 (1994) 173 MR1385525
13 Y Kamishima, S P Tan, Deformation spaces on geometric structures, from: "Aspects of low-dimensional manifolds" (editors Y Matsumoto, S Morita), Adv. Stud. Pure Math. 20, Kinokuniya (1992) 263 MR1208313
14 N J Korevaar, R M Schoen, Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (1993) 561 MR1266480
15 R S Kulkarni, U Pinkall, A canonical metric for Möbius structures and its applications, Math. Z. 216 (1994) 89 MR1273468
16 A Lubotzky, A R Magid, Varieties of representations of finitely generated groups, 336, Amer. Math. Soc (1985) MR818915
17 R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
18 J Sacks, K Uhlenbeck, Minimal immersions of closed Riemann surfaces, Trans. Amer. Math. Soc. 271 (1982) 639 MR654854
19 L P Schaposnik, Spectral data for G–Higgs bundles, PhD thesis, University of Oxford (2013) MR3389247
20 R Schoen, S T Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. 110 (1979) 127 MR541332
21 R A Wentworth, Energy of harmonic maps and Gardiner’s formula, from: "In the tradition of Ahlfors–Bers, IV" (editors D Canary, J Gilman, J Heinonen, H Masur), Contemp. Math. 432, Amer. Math. Soc. (2007) 221 MR2342819
22 M Wolf, Harmonic maps from surfaces to R–trees, Math. Z. 218 (1995) 577 MR1326987
23 M Wolf, On realizing measured foliations via quadratic differentials of harmonic maps to R–trees, J. Anal. Math. 68 (1996) 107 MR1403253
24 M Wolf, Measured foliations and harmonic maps of surfaces, J. Differential Geom. 49 (1998) 437 MR1669653