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Bounded cohomology and totally real subspaces in complex hyperbolic geometry

Published online by Cambridge University Press:  14 September 2011

MARC BURGER  and
ALESSANDRA IOZZI
MARC BURGER
Affiliation:
Department Mathematik, ETH Zentrum, CH-8092 Zürich, Switzerland (email: burger@math.ethz.ch, iozzi@math.ethz.ch)
ALESSANDRA IOZZI
Affiliation:
Department Mathematik, ETH Zentrum, CH-8092 Zürich, Switzerland (email: burger@math.ethz.ch, iozzi@math.ethz.ch)
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Abstract

We characterize representations of finitely generated discrete groups into (the connected component of) the isometry group of a complex hyperbolic space via the pullback of the bounded Kähler class.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 467 - 478
Copyright
Copyright © Cambridge University Press 2011

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References

[1]Bridson, M. R. and Haefliger, A.. Metric Spaces of Non-positive Curvature. Springer, Berlin, 1999.Google Scholar
[2]Burger, M. and Iozzi, A.. Boundary maps in bounded cohomology. Geom. Funct. Anal. 12 (2002), 281–292.Google Scholar
[3]Burger, M. and Iozzi, A.. Bounded Kähler class rigidity of actions on Hermitian symmetric spaces. Ann. Sci. Éc. Norm. Supér. (4) 37(1) (2004), 77–103.CrossRefGoogle Scholar
[4]Burger, M., Iozzi, A., Labourie, F. and Wienhard, A.. Maximal representations of surface groups: symplectic Anosov structures. Pure Appl. Math. Q. 1(3) (2005), 555–601, special issue in memory of Armand Borel, Part 2 of three parts.Google Scholar
[5]Burger, M., Iozzi, A. and Wienhard, A.. Higher Teichmüller spaces: from SL(2,ℝ) to other Lie groups. Handbook of Teichmüller Theory, Vol. 4. European Mathematical Society, 2011.Google Scholar
[6]Burger, M., Iozzi, A. and Wienhard, A.. Surface group representations with maximal Toledo invariant. C. R. Math. Acad. Sci. Paris 336 (2003), 387–390.CrossRefGoogle Scholar
[7]Burger, M., Iozzi, A. and Wienhard, A.. Hermitian symmetric spaces and Kähler rigidity. Transform. Groups 12(1) (2007), 5–32.Google Scholar
[8]Burger, M., Iozzi, A. and Wienhard, A.. Tight embeddings of Hermitian symmetric spaces. Geom. Funct. Anal. 19(3) (2009), 678–721.Google Scholar
[9]Burger, M., Iozzi, A. and Wienhard, A.. Surface group representations with maximal Toledo invariant. Ann. of Math. (2) 172 (2010), 517–566.CrossRefGoogle Scholar
[10]Burger, M. and Monod, N.. Continuous bounded cohomology and applications to rigidity theory. Geom. Funct. Anal. 12 (2002), 219–280.CrossRefGoogle Scholar
[11]Burger, M. and Mozes, S.. CAT(−1)-spaces, divergence groups and their commensurators. J. Amer. Math. Soc. 9(1) (1996), 57–93.Google Scholar
[12]Cartan, E.. Sur les groupes de la géométrie hyperspherique. Comm. Math. Helv. 4 (1932), 158–171.CrossRefGoogle Scholar
[13]Dupont, J. L.. Bounds for characteristic numbers of flat bundles. Algebraic Topology, Aarhus 1978 (Proc. Sympos., Aarhus, 1978) (Lecture Notes in Mathematics, 763). Springer, Berlin, 1979, pp. 109–119.Google Scholar
[14]Ghys, É.. Groupes d’homéomorphismes du cercle et cohomologie bornée. The Lefschetz Centennial Conference, Part III, (Mexico City, 1984) (Contemporary Mathematics, 58). American Mathematical Society, Providence, RI, 1987, pp. 81–106.Google Scholar
[15]Goldman, W. M.. Complex Hyperbolic Geometry (Oxford Mathematical Monographs). The Clarendon Press, Oxford University Press, New York, 1999.Google Scholar
[16]Gromov, M.. Volume and bounded cohomology. Publ. Math. Inst. Hautes Études Sci. 56 (1982), 5–99.Google Scholar
[17]Kaimanovich, V. A.. Double ergodicity of the Poisson boundary and applications to bounded cohomology. Geom. Funct. Anal. 13(4) (2003), 852–861.Google Scholar
[18]Monod, N.. Continuous Bounded Cohomology of Locally Compact Groups (Lecture Notes in Mathematics, 1758). Springer, New York, 2001.Google Scholar
[19]Mostow, G. W.. Self-adjoint groups. Ann. of Math. (2) 62 (1955), 44–55.CrossRefGoogle Scholar
[20]Ramsay, A.. Boolean duals of virtual groups. J. Funct. Anal. 15 (1974), 56–101.CrossRefGoogle Scholar
[21]Zimmer, R. J.. Ergodic Theory and Semisimple Groups. Birkhäuser, Boston, 1984.Google Scholar