Symmetric spaces which are real cohomology spheres

Symmetric Spaces Which Are Real Cohomology Spheres

This is a survey in which we collate some known results using semi-standard techniques, dropping the condition of simple connectivity in Kostant's work [2] and proving Theorem 1. Let M be a compact connected riemannian symmetric space. Then M is a real cohomology (dim M)-sphere if and only if (1) M is an odd dimensional sphere or real projective space; or (2) M = M/Γ where (a) M = S 2 r i X •. ...

Minimal Immersions of Symmetric Spaces into Spheres

Stable Harmonic 2-spheres in Symmetric Spaces

TO = \ I l̂ l'vol. * J M A harmonic map 0 is said to be stable if the second variation of E at (j> is positive semidefinite. That is: for all smooth variations t)\t=0 > 0. Of particular interest is the case where M is the sphere S and N is a Riemannian symmetric space G/K. In this setting harmonic maps are branched minimal immersions, or the finite ...

The Integral Cohomology Algebras of Ordered Configuration Spaces of Spheres

We compute the cohomology algebras of spaces of ordered point configurations on spheres, F (S, n), with integer coefficients. For k = 2 we describe a product structure that splits F (S, n) into well-studied spaces. For k > 2 we analyze the spectral sequence associated to a classical fiber map on the configuration space. In both cases we obtain a complete and explicit description of the integer ...

Configuration Spaces of Complex and Real Spheres

We study the GIT-quotient of the Cartesian ppower of a projective space modulo the projective orthogonal group. A classical isomorphism of this group with the Inversive group of birational transformations of the projective space of one dimension less allows one to interpret these spaces as configuration spaces of complex or real spheres.