Flats and the flat torus theorem in systolic spaces.

DOI10.2140/gt.2009.13.661zbMath1228.20033OpenAlexW1988879833MaRDI QIDQ1006136

Tomasz Elsner

Publication date: 19 March 2009

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/gt.2009.13.661

zbMATH Keywords

minimal surfacessystolic complexessystolic groupsflat tori

Mathematics Subject Classification ID

Geometric group theory (20F65) Topological methods in group theory (57M07) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Hyperbolic groups and nonpositively curved groups (20F67) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (15)

Boundaries of systolic groups. ⋮ The triangle groups (2, 4, 5) and (2, 5, 5) are not systolic ⋮ Solvable Subgroup Theorem for simplicial nonpositive curvature ⋮ Normal subgroups of SimpHAtic groups ⋮ Systolic complexes and group presentations ⋮ Graphical complexes of groups ⋮ Graphs with convex balls ⋮ Hyperbolic isometries and boundaries of systolic complexes ⋮ Quasi-flats in systolic complexes ⋮ Tits alternative for groups acting properly on 2-dimensional recurrent complexes ⋮ A combination theorem for combinatorially non-positively curved complexes of hyperbolic groups ⋮ Metric systolicity and two-dimensional Artin groups ⋮ Square complexes and simplicial nonpositive curvature ⋮ Homotopical systole and hyperbolicity ⋮ Systolizing buildings

Cites Work

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• Simplicial nonpositive curvature
• Nonpositively curved 2-complexes with isolated flats.
• Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi).
• Filling invariants of systolic complexes and groups.
• Systolic groups acting on complexes with no flats are word-hyperbolic
• Isometries of systolic spaces

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