The zero-norm subspace of bounded cohomology

  • T. Soma

    Tokyo Denki University, Japan


Let Σ\Sigma be a closed, orientable surface of genus > 1. In this paper, non-trivial elements α\alpha of the third bounded cohomology Hb3(Σ;R)H_b^3(\Sigma;\bf {R}) with α=0\Vert \alpha \Vert = 0 are given constructively by using both a hyperbolic metric and a singular euclidean metric on Σ×R\Sigma \times \bf {R} . Furthermore, it is shown that the dimension of the subspace N3(Σ)N^3(\Sigma) of Hb3(Σ;R)H_b^3(\Sigma;\bf {R}) consisting of zero-norm elements is the cardinality of the continuum.

Cite this article

T. Soma, The zero-norm subspace of bounded cohomology. Comment. Math. Helv. 72 (1997), no. 4, pp. 582–592

DOI 10.1007/S000140050035