Homogeneous Spaces of Nonreductive Type That Do Not Model Any Compact Manifold

  • Yosuke Morita

    University of Tokyo, Japan

Abstract

We give necessary conditions for the existence of a compact manifold locally modeled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and nonreductive cases. For example, we prove that there does not exist a compact manifold locally modeled on a positive-dimensional coadjoint orbit of a real linear solvable algebraic group.

Cite this article

Yosuke Morita, Homogeneous Spaces of Nonreductive Type That Do Not Model Any Compact Manifold. Publ. Res. Inst. Math. Sci. 53 (2017), no. 2, pp. 287–298

DOI 10.4171/PRIMS/53-2-3