JournalscmhVol. 87, No. 3pp. 705–725

Reconstructing quasimorphisms from associated partial orders and a question of Polterovich

  • Gabi Ben Simon

    ETH Zürich, Switzerland
  • Tobias Hartnick

    Technion - Israel Institute of Technology, Haifa, Israel
Reconstructing quasimorphisms from associated partial orders  and a question of Polterovich cover
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Abstract

We show that every continuous homogeneous quasimorphism on a finite-dimensional 1-connected simple Lie group arises as the relative growth of some 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.

Cite this article

Gabi Ben Simon, Tobias Hartnick, Reconstructing quasimorphisms from associated partial orders and a question of Polterovich. Comment. Math. Helv. 87 (2012), no. 3, pp. 705–725

DOI 10.4171/CMH/266