Algebraic & Geometric Topology Volume 24, issue 7 (2024)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

A closed ball compactification of a maximal component via cores of trees

Giuseppe Martone, Charles Ouyang and Andrea Tamburelli

Algebraic & Geometric Topology 24 (2024) 3693–3717

DOI: 10.2140/agt.2024.24.3693

Bibliography

1	D Alessandrini, Tropicalization of group representations, Algebr. Geom. Topol. 8 (2008) 279 MR2443230
2	D Alessandrini, B Collier, The geometry of maximal components of the PSp(4, ℝ) character variety, Geom. Topol. 23 (2019) 1251 MR3956893
3	M Bestvina, Degenerations of the hyperbolic space, Duke Math. J. 56 (1988) 143 MR932860
4	F Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988) 139 MR931208
5	G W Brumfiel, The real spectrum compactification of Teichmüller space, from: "Geometry of group representations", Contemp. Math. 74, Amer. Math. Soc. (1988) 51 MR957511
6	M Burger, M B Pozzetti, Maximal representations, non-Archimedean Siegel spaces, and buildings, Geom. Topol. 21 (2017) 3539 MR3692972
7	M Burger, A Iozzi, A Parreau, M B Pozzetti, A structure theorem for geodesic currents and length spectrum compactifications, preprint (2017) arXiv:1710.07060
8	M Burger, A Iozzi, A Parreau, M B Pozzetti, Currents, systoles, and compactifications of character varieties, Proc. Lond. Math. Soc. 123 (2021) 565 MR4368682
9	M Burger, A Iozzi, A Parreau, M B Pozzetti, The real spectrum compactification of character varieties: characterizations and applications, C. R. Math. Acad. Sci. Paris 359 (2021) 439 MR4278899
10	M Burger, A Iozzi, A Parreau, M B Pozzetti, Weyl chamber length compactification of the PSL(2, ℝ) × PSL(2, ℝ) maximal character variety, preprint (2021) arXiv:2112.13624
11	M Burger, A Iozzi, A Parreau, M B Pozzetti, Positive crossratios, barycenters, trees and applications to maximal representations, Groups Geom. Dyn. 18 (2024) 799 MR4760263
12	B Collier, Maximal Sp(4, ℝ) surface group representations, minimal immersions and cyclic surfaces, Geom. Dedicata 180 (2016) 241 MR3451467
13	B Collier, N Tholozan, J Toulisse, The geometry of maximal representations of surface groups into SO₀(2,n), Duke Math. J. 168 (2019) 2873 MR4017517
14	C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
15	M Duchin, C J Leininger, K Rafi, Length spectra and degeneration of flat metrics, Invent. Math. 182 (2010) 231 MR2729268
16	J Eells Jr., J H Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964) 109 MR164306
17	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
18	A Fathi, F Laudenbach, V Poénaru, Thurston’s work on surfaces, 48, Princeton Univ. Press (2012) MR3053012
19	V Fock, A Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006) 1 MR2233852
20	F P Gardiner, H Masur, Extremal length geometry of Teichmüller space, Complex Variables Theory Appl. 16 (1991) 209 MR1099913
21	W M Goldman, Topological components of spaces of representations, Invent. Math. 93 (1988) 557 MR952283
22	V Guirardel, Cœur et nombre d’intersection pour les actions de groupes sur les arbres, Ann. Sci. École Norm. Sup. 38 (2005) 847 MR2216833
23	V Guirardel, G Levitt, JSJ decompositions of groups, 395, Soc. Math. France (2017) MR3758992
24	P Hartman, On homotopic harmonic maps, Canadian J. Math. 19 (1967) 673 MR214004
25	J Hubbard, H Masur, Quadratic differentials and foliations, Acta Math. 142 (1979) 221 MR523212
26	K Krasnov, J M Schlenker, Minimal surfaces and particles in 3–manifolds, Geom. Dedicata 126 (2007) 187 MR2328927
27	F Labourie, Cyclic surfaces and Hitchin components in rank 2, Ann. of Math. 185 (2017) 1 MR3583351
28	I Le, Higher laminations and affine buildings, Geom. Topol. 20 (2016) 1673 MR3523066
29	G Levitt, Foliations and laminations on hyperbolic surfaces, Topology 22 (1983) 119 MR683752
30	J C Loftin, Affine spheres and convex ℝℙⁿ–manifolds, Amer. J. Math. 123 (2001) 255 MR1828223
31	J Loftin, A Tamburelli, M Wolf, Limits of cubic differentials and buildings, preprint (2022) arXiv:2208.07532
32	G Martone, Positive configurations of flags in a building and limits of positive representations, Math. Z. 293 (2019) 1337 MR4024589
33	G Martone, Sequences of Hitchin representations of tree-type, preprint (2019) arXiv:1910.13585
34	G Mess, Lorentz spacetimes of constant curvature, Geom. Dedicata 126 (2007) 3 MR2328921
35	J W Morgan, J P Otal, Relative growth rates of closed geodesics on a surface under varying hyperbolic structures, Comment. Math. Helv. 68 (1993) 171 MR1214228
36	J W Morgan, P B Shalen, Valuations, trees, and degenerations of hyperbolic structures, I, Ann. of Math. 120 (1984) 401 MR769158
37	K Oikawa, Notes on conformal mappings of a Riemann surface onto itself, Kōdai Math. Sem. Rep. 8 (1956) 23 MR80730
38	J P Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. 131 (1990) 151 MR1038361
39	C Ouyang, High-energy harmonic maps and degeneration of minimal surfaces, Geom. Topol. 27 (2023) 1691 MR4621919
40	C Ouyang, A Tamburelli, Limits of Blaschke metrics, Duke Math. J. 170 (2021) 1683 MR4278667
41	C Ouyang, A Tamburelli, Length spectrum compactification of the SO₀(2,3)–Hitchin component, Adv. Math. 420 (2023) 108997 MR4568060
42	A Parreau, Compactification d’espaces de représentations de groupes de type fini, Math. Z. 272 (2012) 51 MR2968214
43	A Parreau, Invariant weakly convex cocompact subspaces for surface groups in A₂–buildings, Trans. Amer. Math. Soc. 375 (2022) 2293 MR4391719
44	F Paulin, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, Invent. Math. 94 (1988) 53 MR958589
45	R M Schoen, The role of harmonic mappings in rigidity and deformation problems, from: "Complex geometry", Lecture Notes in Pure and Appl. Math. 143, Dekker (1993) 179 MR1201611
46	R K Skora, Splittings of surfaces, J. Amer. Math. Soc. 9 (1996) 605 MR1339846
47	M Wolf, The Teichmüller theory of harmonic maps, J. Differential Geom. 29 (1989) 449 MR982185
48	M Wolf, Harmonic maps from surfaces to ℝ–trees, Math. Z. 218 (1995) 577 MR1326987