Nonimmersions of complex Grassmann manifolds

A Star Product for Complex Grassmann Manifolds

We explicitly construct a star product for the complex Grassmann manifolds using the method of phase space reduction. Functions on C(p+q)·p ∗, the space of (p + q)× p matrices of rank p, invariant under the right action of Gl(p, C) can be regarded as functions on the Grassmann manifold Gp,q(C), but do not form a subalgebra whereas functions only invariant under the unitary subgroup U(p) ⊂ Gl(p,...

Differential Calculus on Quantum Complex Grassmann Manifolds I: Construction

Covariant first order differential calculus over quantum complex Grassmann manifolds is considered. It is shown by a Pusz–Woronowicz type argument that under restriction to calculi close to classical Kähler differentials there exist exactly two such calculi for the homogeneous coordinate ring. Complexification and localization procedures are used to induce covariant first order differential cal...

Space Forms of Grassmann Manifolds

Cobordism independence of Grassmann manifolds

This paper is a continuation of the ongoing study of cobordism of Grassmann manifolds. Let F denote one of the division rings R of reals, C of complex numbers, or H of quaternions. Let t = dimRF . Then the Grassmannian manifold Gk(F) is defined to be the set of all k-dimensional (left) subspaces of Fn+k. Gk(F) is a closed manifold of real dimension nkt. Using the orthogonal complement of a subs...

Characteristic Classes on Grassmann Manifolds

In this paper, we use characteristic classes of the canonical vector bundles and the Poincaré dualality to study the structure of the real homology and cohomology groups of oriented Grassmann manifold G(k, n). Show that for k = 2 or n ≤ 8, the cohomology groups H∗(G(k, n),R) are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles. In these cases, the Poinc...