Title: On the fundamental group of semi-Riemannian manifolds with positive curvature operator,
Abstract: This paper presents an investigation of the relation between some positivity
of the curvature and the finiteness of fundamental groups in semi-Riemannian
geometry. We consider semi-Riemannian submersions $\pi : (E, g) \rightarrow (B,
-g_{B}) $ under the condition with $(B, g_{B})$ Riemannian, the fiber closed
Riemannian, and the horizontal distribution integrable. Then we prove that, if
the lightlike geodesically complete or timelike geodesically complete
semi-Riemannian manifold $E$ has some positivity of curvature, then the
fundamental group of the fiber is finite. Moreover we construct an example of
semi-Riemannian submersions with some positivity of curvature, non-integrable
horizontal distribution, and the finiteness of the fundamental group of the
fiber.