The zero-norm subspace of bounded cohomology

  • T. Soma

    Tokyo Denki University, Japan


Let be a closed, orientable surface of genus > 1. In this paper, non-trivial elements of the third bounded cohomology with are given constructively by using both a hyperbolic metric and a singular euclidean metric on . Furthermore, it is shown that the dimension of the subspace of 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