分野別セミナー

Let M be a non-compact connected manifold with a cocompact and properly discontinuous action of a group G. We define the integral in the bounded de Rham cohomology of M, and establish the Hopf-Poincaré theorem for M. Then we apply it to prove that a bounded and tame vector field on M must have inifinitely many zeros whenever M/G is orientable, the Euler characteristic of M/G is non-trivial, and G is an amenable group having an element of infinite order.

This is joint work with Tsuyoshi Kato and Mitsunobu Tsutaya.