Reconstructing quasimorphisms from associated partial orders and a question of Polterovich

Details Reconstructing quasimorphisms from associated partial orders and a question of Polterovich Reconstructing quasimorphisms from associated partial orders and a question of Polterovich

2008-11-17

arxiv.org/abs/0811.2608v4

Mathematics

Group Theory

Minor errors corrected. The main theorem is now proved for arbitrary continuous bi-invariant partial orders. To appear in Comm

Scientific 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.

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