Bridge genus and braid genus of lens space

The bridge genus and the braid genus are invariants of a closed connected orientable 3-manifold introduced by A. Kawauchi. The Heegaard genus, the bridge genus and the braid genus are linearly independent as invariants of a closed connected orientable 3-manifold. In this paper, we calculate the bridge genus and the braid genus for some lens spaces, and we give the upper bounds of the braid genus for all lens spaces.