Simplicial volume of ℚ–rank one locally symmetric spaces covered by the product of ℝ–rank one symmetric spaces
Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 1165-1181
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In this paper, we show that the simplicial volume of ℚ–rank one locally symmetric spaces covered by the product of ℝ–rank one symmetric spaces is strictly positive.

DOI : 10.2140/agt.2012.12.1165
Keywords: simplicial volume, symmetric space, arithmetic lattice

Kim, Sungwoon  1   ; Kim, Inkang  1

1 School of Mathematics, KIAS, Heogiro 85, Dongdaemun-gu, Seoul 130-722, Republic of Korea
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Kim, Sungwoon; Kim, Inkang. Simplicial volume of ℚ–rank one locally symmetric spaces covered by the product of ℝ–rank one symmetric spaces. Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 1165-1181. doi: 10.2140/agt.2012.12.1165

[1] G Besson, G Courtois, S Gallot, Volume et entropie minimale des espaces localement symétriques, Invent. Math. 103 (1991) 417

[2] A Borel, Introduction aux groupes arithmétiques, 1341, Hermann (1969) 125

[3] M Bucher-Karlsson, Simplicial volume of locally symmetric spaces covered by SL3R∕SO(3), Geom. Dedicata 125 (2007) 203

[4] M Bucher-Karlsson, The proportionality constant for the simplicial volume of locally symmetric spaces, Colloq. Math. 111 (2008) 183

[5] M Bucher, I Kim, S Kim, Proportionality principle for the simplicial volume of Q–rank one locally symmetric spaces, in preparation

[6] C Connell, B Farb, The degree theorem in higher rank, J. Differential Geom. 65 (2003) 19

[7] C Connell, B Farb, Minimal entropy rigidity for lattices in products of rank one symmetric spaces, Comm. Anal. Geom. 11 (2003) 1001

[8] C Connell, B Farb, Some recent applications of the barycenter method in geometry, from: "Topology and geometry of manifolds (Athens, GA, 2001)", Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 19

[9] J L Dupont, Simplicial de Rham cohomology and characteristic classes of flat bundles, Topology 15 (1976) 233

[10] P B Eberlein, Geometry of nonpositively curved manifolds, , University of Chicago Press (1996)

[11] R Frigerio, (Bounded) continuous cohomology and Gromov’s proportionality principle, Manuscripta Math. 134 (2011) 435

[12] M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982) 5

[13] H Inoue, K Yano, The Gromov invariant of negatively curved manifolds, Topology 21 (1982) 83

[14] J F Lafont, B Schmidt, Simplicial volume of closed locally symmetric spaces of non-compact type, Acta Math. 197 (2006) 129

[15] E Leuzinger, An exhaustion of locally symmetric spaces by compact submanifolds with corners, Invent. Math. 121 (1995) 389

[16] E Leuzinger, On polyhedral retracts and compactifications of locally symmetric spaces, Differential Geom. Appl. 20 (2004) 293

[17] C Löh, Measure homology and singular homology are isometrically isomorphic, Math. Z. 253 (2006) 197

[18] C Löh, l1–Homology and Simplicial Volume, PhD thesis, WWU Münster (2007)

[19] C Löh, R Sauer, Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume, J. Topol. 2 (2009) 193

[20] C Löh, R Sauer, Simplicial volume of Hilbert modular varieties, Comment. Math. Helv. 84 (2009) 457

[21] R P Savage Jr., The space of positive definite matrices and Gromov’s invariant, Trans. Amer. Math. Soc. 274 (1982) 239

[22] W Thurston, Geometry and Topology of 3–manifolds, lecture notes (1978)

[23] R J Zimmer, Ergodic theory and semisimple groups, 81, Birkhäuser (1984)

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