Volume 19, issue 6 (2015)

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

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

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 Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Bounded cohomology via partial differential equations, I

Tobias Hartnick and Andreas Ott

Geometry & Topology 19 (2015) 3603–3643
1 G Ben Simon, M Burger, T Hartnick, A Iozzi, A Wienhard, On weakly maximal representations of surface groups, preprint (2013) arXiv:1305.2620
2 M Bestvina, K Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002) 69 MR1914565
3 S J Bloch, Higher regulators, algebraic $K$–theory, and zeta functions of elliptic curves, CRM Monograph Series 11, Amer. Math. Soc. (2000) MR1760901
4 R Brooks, Some remarks on bounded cohomology, from: "Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook conference" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 53 MR624804
5 M Bucher-Karlsson, Finiteness properties of characteristic classes of flat bundles, Enseign. Math. 53 (2007) 33 MR2343344
6 M Bucher, M Burger, A Iozzi, A dual interpretation of the Gromov–Thurston proof of Mostow rigidity and volume rigidity for representations of hyperbolic lattices, from: "Trends in harmonic analysis" (editor M A Picardello), Springer INdAM Ser. 3, Springer, Milan (2013) 47 MR3026348
7 M Bucher, N Monod, The norm of the Euler class, Math. Ann. 353 (2012) 523 MR2915547
8 M Burger, A Iozzi, Bounded Kähler class rigidity of actions on Hermitian symmetric spaces, Ann. Sci. École Norm. Sup. 37 (2004) 77 MR2050206
9 M Burger, A Iozzi, Bounded cohomology and totally real subspaces in complex hyperbolic geometry, Ergodic Theory Dynam. Systems 32 (2012) 467 MR2901355
10 M Burger, A Iozzi, A Wienhard, Tight homomorphisms and Hermitian symmetric spaces, Geom. Funct. Anal. 19 (2009) 678 MR2563767
11 M Burger, A Iozzi, A Wienhard, Surface group representations with maximal Toledo invariant, Ann. of Math. 172 (2010) 517 MR2680425
12 M Burger, A Iozzi, A Wienhard, Higher Teichmüller spaces: from $\mathrm{SL}(2,\mathbb{R}$ to other Lie groups, from: "Handbook of Teichmüller theory, IV" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 19, Eur. Math. Soc., Zürich (2014) 539 MR3289711
13 M Burger, N Monod, Bounded cohomology of lattices in higher rank Lie groups, J. Eur. Math. Soc. $($JEMS$)$ 1 (1999) 199 MR1694584
14 M Burger, N Monod, Continuous bounded cohomology and applications to rigidity theory, Geom. Funct. Anal. 12 (2002) 219 MR1911660
15 M Burger, N Monod, On and around the bounded cohomology of $\mathrm{SL}_2$, from: "Rigidity in dynamics and geometry" (editors M Burger, A Iozzi), Springer, Berlin (2002) 19 MR1919394
16 C Carathéodory, Calculus of variations and partial differential equations of the first order, I: Partial differential equations of the first order, Holden-Day (1965) MR0192372
17 I Chatterji, T Fernós, A Iozzi, The median class and superrigidity of actions on CAT(0) cube complexes, preprint (2012) arXiv:1212.1585
18 J L Dupont, Bounds for characteristic numbers of flat bundles, from: "Algebraic topology" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer, Berlin (1979) 109 MR561216
19 M Entov, L Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. 2003 (2003) 1635 MR1979584
20 D B A Epstein, K Fujiwara, The second bounded cohomology of word-hyperbolic groups, Topology 36 (1997) 1275 MR1452851
21 K Fujiwara, M Bestvina, K Bromberg, Bounded cohomology with coefficients in uniformly convex Banach spaces, preprint (2013) arXiv:1306.1542
22 A B Goncharov, Geometry of configurations, polylogarithms, and motivic cohomology, Adv. Math. 114 (1995) 197 MR1348706
23 R I Grigorchuk, Some results on bounded cohomology, from: "Combinatorial and geometric group theory" (editors A J Duncan, N D Gilbert, J Howie), London Math. Soc. Lecture Note Ser. 204, Cambridge Univ. Press (1995) 111 MR1320279
24 M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982) 5 MR686042
25 U Hamenstädt, Isometry groups of proper hyperbolic spaces, Geom. Funct. Anal. 19 (2009) 170 MR2507222
26 U Hamenstädt, Isometry groups of proper $\mathrm{CAT}(0)$–spaces of rank one, Groups Geom. Dyn. 6 (2012) 579 MR2961285
27 T Hartnick, A Ott, Surjectivity of the comparison map in bounded cohomology for Hermitian Lie groups, Int. Math. Res. Not. 2012 (2012) 2068 MR2920824
28 T Hartnick, A Ott, Perturbations of the Spence–Abel equation and deformations of the dilogarithm function, in preparation (2015)
29 M Hull, D Osin, Induced quasi-cocycles on groups with hyperbolically embedded subgroups, preprint (2012) arXiv:1203.5436
30 N V Ivanov, Foundations of the theory of bounded cohomology, Zap. Nauchn. Sem. LOMI 143 (1995) 69
31 B E Johnson, Cohomology in Banach algebras, Memoirs of the American Mathematical Society 127, Amer. Math. Soc. (1972) MR0374934
32 W Kerby, On infinite sharply multiply transitive groups, Hamburger Mathematische Einzelschriften 6, Vandenhoeck & Ruprecht (1974) 71 MR0384938
33 A W Knapp, Lie groups beyond an introduction, Progress in Mathematics 140, Birkhäuser (2002) MR1920389
34 J F Lafont, B Schmidt, Simplicial volume of closed locally symmetric spaces of non-compact type, Acta Math. 197 (2006) 129 MR2285319
35 J M Lee, Manifolds and differential geometry, Graduate Studies in Mathematics 107, Amer. Math. Soc. (2009) MR2572292
36 I Mineyev, Bounded cohomology characterizes hyperbolic groups, Q. J. Math. 53 (2002) 59 MR1887670
37 N Monod, Continuous bounded cohomology of locally compact groups, Lecture Notes in Mathematics 1758, Springer, Berlin (2001) MR1840942
38 N Monod, An invitation to bounded cohomology, from: "International Congress of Mathematicians, II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc., Zürich (2006) 1183 MR2275641
39 N Monod, On the bounded cohomology of semi-simple groups, $S$–arithmetic groups and products, J. Reine Angew. Math. 640 (2010) 167 MR2629693
40 N Monod, Equivariant measurable liftings, Fund. Math. 230 (2015) 149 MR3337223
41 N Monod, Y Shalom, Cocycle superrigidity and bounded cohomology for negatively curved spaces, J. Differential Geom. 67 (2004) 395 MR2153026
42 N Monod, Y Shalom, Orbit equivalence rigidity and bounded cohomology, Ann. of Math. 164 (2006) 825 MR2259246
43 H Pieters, Continuous cohomology of the isometry group of hyperbolic space realizable on the boundary, preprint (2015) arXiv:1507.04915
44 L Polterovich, Growth of maps, distortion in groups and symplectic geometry, Invent. Math. 150 (2002) 655 MR1946555