Geometric cycles and bounded cohomology for a cocompact lattice in \(\mathrm{SL}_n(\mathbb{R})\)

DOI10.1007/s00209-022-03006-7zbMath1504.57047arXiv2010.08594OpenAlexW4229080123MaRDI QIDQ2672702

Yanyan Li

Publication date: 13 June 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.08594

zbMATH Keywords

submanifoldGromov normhomology class

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Differential geometry of symmetric spaces (53C35) Other matrix groups over fields (20H20) Homotopy groups of topological groups and homogeneous spaces (57T20) Realizing cycles by submanifolds (57R95)

Related Items (1)

Homological norms on nonpositively curved manifolds

Cites Work

• Geometric construction of cohomology for arithmetic groups. I
• Some remarks on the simplicial volume of nonpositively curved manifolds
• Simplicial volume of closed locally symmetric spaces of non-compact type
• Flat cycles in the homology of \(\Gamma \setminus SL_m \mathbb{R} / SO(m)\)
• Volume and bounded cohomology
• The Gromov invariant of negatively curved manifolds
• Lectures on hyperbolic geometry
• Barycentric straightening and bounded cohomology
• Geometric cycles and characteristic classes of manifold bundles (with an appendix by M. Krannich)
• Positivity of simplicial volume for nonpositively curved manifolds with a Ricci-type curvature condition
• Simplicial volume of locally symmetric spaces covered by \(\mathrm{SL}_{3} \mathbb R/\mathrm{SO}(3)\)
• On splitting rank of non-compact-type symmetric spaces and bounded cohomology
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