We show that the Kervaire invariant one elements θ_jϵπ_2^j+1-2S^0 exist only for j≤ 6. By
Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist …

In 1960, Kervaire [11] introduced an invariant for almost framed (4k+ 2)-manifolds,(k# 0, 1,
3), and proved that it was zero for framed 10-manifolds, which was a key step in his …

M. Kervaire in [4], F. Peterson and myself in [1], and W. Browder in [3] defined numerical
invariants for various classes of 2n-manifolds roughly as follows: Suppose M is a closed …

Let X be a compact complex manifold of (complex) dimension n, and ξ a holomorphic vector
bundle over X. We shall denote by Ω (ζ) the sheaf of germs of holomorphic sections of f, and …

LET A4 be a compact complex manifold of complex dimension n, with real Chern classes
Cl,...) c,. The Riemann-Roth theorem provides a number of relations between the Hodge …

1. Introduction and statement of the results. We consider a compact symplectic manifold (P,
to) with symplectic structure to, which is a closed and nondegenerate 2-form. For example …

In general, the existence of a holomorphic vector field with zeros on a compact complex
manifold imposes restrictions on the topology and numerical characters of the manifold. For …

We show that in every dimension greater than or equal to 4, there exist compact Kaehler
manifolds which do not have the homotopy type of projective complex manifolds. Thus they …

Our main purpose is to prove Hartshorne's conjecture [5]: THEOREM 8 (Hp). Every
irreducible n-dimensional non-singular projective variety with ample tangent bundle defined …

Let (Mn, g) be a n-dimensional compact hermitian manifold, with n> 2.(M, g) will be called
projectively flat, if its curvature matrix is of the form 0= a/n, where a is a (1, l)-form. Note that …