Shin-ichi Matsumura

Atiyah classes and ellipticity of Oka manifolds

We prove that every weakly pseudoconvex Oka manifold admitting a positive line bundle is elliptic in the sense of Gromov, thereby proving Gromov's ellipticity conjecture. The proof establishes a cohomological construction of local sprays. Given a bundle morphism $\varphi\colon E\to T_X$, we introduce quadratic $\varphi...