Circular groups, planar groups, and the Euler class
By Danny Calegari. 2004
75 citations recorded by the source corpus.
We study groups of C 1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly- orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that certain generalized braid groups are circularly-orderable. We also show that the Euler class of C ∞ diffeomorphisms of the plane is an unbounded class, and that any closed surface group of genus > 1 admits a C ∞ action with arbitrary Euler class. On the other hand, we show that Z ⊕ Z actions satisfy a homological rigidity property: every orientation- preserving C 1 action of Z ⊕ Z on the plane has trivial Euler class. This gives the complete homological classification of surface group actions on R 2
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fae3cd7ed8b77d4170b5cd37bb1c833fd8afbf99
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Foliations and the Geometry of 3-Manifolds (2007, background): “The material in the next few sections borrows substantially from [36].”
- Algebraic and topological properties of big mapping class groups (2017, unknown): “[12]), taut foliations of 3-manifolds (e.”
- Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group (2014, background): “R 2 Cantor /: Dans [9], Calegari montre qu’il existe un morphisme injectif de dans Homeo .”