Space of group orderings, quasi morphisms and bounded cohomology

2010/06/29 by Tetsuya Ito, Ito, Tetsuya
Mathematics · #20F60 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20F60

paper · pdf · doi:10.48550/arxiv.1006.5491

14 pages, no figures, The statement of Theorem 1 is corrected

openalex publication_date 2010/06/29 · arxiv created 2010/07/06 · arxiv updated 2010/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a group G, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.

Citations

• Braid ordering and knot genus

Related

• Low-dimensional bounded cohomology and extensions of groups
• The topology on the space of left orderings of a group
• Quasi-morphisms on Free Groups
• Orders on groups, and spectral spaces of lattice-groups
• Faithful actions of automorphisms on the space of orderings of a group