Abstract
Let D2 be the open unit disc in the Euclidean plane and let G:=WD Diff.D2; area/ be the group of smooth compactly supported area-preserving diffeomorphisms of D2. For every natural number k we construct an injective homomorphism Z k → G, which is bi-Lipschitz with respect to the word metric on Zk and the autonomous metric on G. We also show that the space of homogeneous quasimorphisms vanishing on all autonomous diffeomorphisms in the above group is infinite-dimensional.
Original language | English |
---|---|
Pages (from-to) | 795-816 |
Number of pages | 22 |
Journal | Algebraic and Geometric Topology |
Volume | 13 |
Issue number | 2 |
DOIs | |
State | Published - 11 Apr 2013 |
Externally published | Yes |
Keywords
- Area-preserving diffeomorphisms
- Bi-invariant metrics
- Braid groups
- Quasi-isometric embeddings
- Quasimorphisms
ASJC Scopus subject areas
- Geometry and Topology