Projective limits of paratopological vector spaces

Projective limits of topological vector spaces

Projective embedding of projective spaces

In this paper, embeddings φ : M → P from a linear space (M,M) in a projective space (P,L) are studied. We give examples for dimM > dimP and show under which conditions equality holds. More precisely, we introduce properties (G) (for a line L ∈ L and for a plane E ⊂ M it holds that |L ∩ φ(M)| 6 = 1) and (E) (φ(E) = φ(E) ∩ φ(M), whereby φ(E) denotes the by φ(E) generated subspace of P ). If (G) a...

Mirror Symmetry for Concavex Vector Bundles on Projective Spaces

Let V + = ⊕i∈IO(ki) and V − = ⊕j∈JO(−lj) be vector bundles on P s with ki and lj positive integers. Suppose X ι →֒ Ps is the zero locus of a generic section of V + and Y is a projective manifold such that X j →֒ Y with normal bundle NX/Y = ι ∗(V −). The relations between Gromov-Witten theories of X and Y are studied here by means of a suitably defined equivariant Gromov-Witten theory in Ps. We ap...

On Stable Vector Bundles over Real Projective Spaces

If X is a connected, finite CJF-complex, we can define iKO)~iX) to be [X, BO] (base-point preserving homotopy classes of maps). Recall [2] that if xEiKO)~iX), the geometrical dimension of x (abbreviated g.dim x) can be defined to be the smallest nonnegative integer k such that a representative of x factors through BO(k). If $ is a vector bundle over X, the class in (PO)~(X) of a classifying map...

Stably extendible vector bundles over the quaternionic projective spaces

We show that, if a quaternionic k-dimensional vector bundle l' over the quaternionic projective space Hpn is stably extendible and its non-zero top Pontrjagin class is not zero mod 2, then l' is stably equivalent to the Whitney sum of k quaternionic line bundles provided k S; n.