Reconstructing Quasimorphisms from Associated Partial Orders and a Question of Polterovich
- Working Paper
We show that every continuous homogeneous quasimorphism on a finite-dimensional 1-connected simple Lie group arises as the relative growth of any continuous bi-invariant partial order on that group. More generally we show, that an arbitrary homogeneous quasimorphism can be reconstructed as the relative growth of a partial order subject to a certain sandwich condition. This provides a link between invariant orders and bounded cohomology and allows the concrete computation of relative growth for finite dimensional simple Lie groups as well as certain infinite-dimensional Lie groups arising from symplectic geometry. Show more
Pages / Article No.
Organisational unit08802 - Iozzi, Alessandra (Tit.-Prof.)
03513 - Salamon, Dietmar (emeritus)
02000 - Dep. Mathematik / Dep. of Mathematics
NotesSubmitted 17 November 2008 (v1), Last revised 5 October 2010 (this version, v4).
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