Abstract
We give the first complete proof of the strict positivity of the simplicial volume of compact locally symmetric spaces covered by \({\rm SL}_{3}{\mathbb{R}}/{\rm SO}(3)\) and show why the proof in [Savage RP, Trans Amer Math Soc 274(1):239–263, 1982] is incorrect.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bucher-Karlsson, M.: Characteristic classes and bounded cohomology, Ph.D. thesis, ETHZ (2004)
Bucher-Karlsson, M.: A detailed study of Savage’s paper “The space of positive definite matrices and Gromov’s invariant”, preprint (2005)
Connell C., Farb B. (2003) The degree theorem in higher rank. J. Diff. Geom. 65(1): 19–59
Dupont J. (1976) Simplicial de Rham cohomology and characteristic classes of flat bundles. Topology 15: 233–245
de la Harpe, P.: On Hilbert’s metric for simplices. In: Geometric group theory, vol. 1 (Sussex, 1991). London Math. Soc. Lecture Note Ser. vol. 181, pp. 97–119. Cambridge University Press, Cambridge (1999)
Inoue H., Yano K. (1982) The Gromov invariant of negatively curved manifolds. Topology 21: 83–89
Lafont J.-F., Schmidt B. (2006) Simplicial volume of closed locally symmetric spaces of non-compact type. Acta Math. 197(1): 129–143
Lang, S.: Fundamentals of Differential Geometry. Graduate texts in mathematics 191, Springer-Verlag (1999)
Savage R.P. Jr. (1982) The space of positive definite matrices and Gromov’s invariant. Trans. Amer. Math. Soc. 274(1): 239–263
Thurston, W.: Geometry and Topology of 3-Manifolds. Lecture Notes, Princeton University (1978)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bucher-Karlsson, M. Simplicial volume of locally symmetric spaces covered by \({\rm SL}_{3}{\mathbb{R}}/{\rm SO}(3)\) . Geom Dedicata 125, 203–224 (2007). https://doi.org/10.1007/s10711-007-9158-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-007-9158-4