Symplectic Cobordism Research Articles

On the Image of Symplectic Cobordism in Unoriented Cobordism

It is shown in this paper that all 16th powers of unoriented cobordism classes can be represented by stably almost symplectic manifolds. The generators are coefficients in the expansion of a Conner-Floyd characteristic class of the symplectification of a tensor product of symplectic line bundles.

On the image of symplectic cobordism in unoriented cobordism

It is shown in this paper that all 16th powers of unoriented cobordism classes can be represented by stably almost symplectic manifolds. The generators are coefficients in the expansion of a Conner-Floyd characteristic class of the symplectification of a tensor product of symplectic line bundles.

Divisibility conditions on characteristic numbers of stably symplectic manifolds

It is shown that every cohomology characteristic number of an $8k + 4$ [resp. $16k + 8$] dimensional stably symplectic manifold is divisible by 4 [resp. 2] and that certain characteristic numbers of $2$-dimensional stably symplectic manifolds are divisible by 2 and 4. The proofs depend on symplectic cobordism operations. Using explicit manifold constructions of Stong [

Stiefel-Whitney numbers of quaternionic and related manifolds

There is considered the image of the symplectic cobordism ring $\Omega _\ast ^{SP}$ in the unoriented cobordism ring ${N_\ast }$. A polynomial subalgebra of ${N_\ast }$ is exhibited, with all generators in dimensions divisible by 16, such that the image is contained in the polynomial subalgebra. The methods combine the $K$-theory characteristic numbers as used by Stong with the use of the Landweber-Novikov ring.

On the symplectic cobordism ring

On the symplectic cobordism ring

ON SYMPLECTIC COBORDISMS

In the article, the method of spherical reconstructions of smooth manifolds is applied to the computation of some groups of symplectic cobordisms. Namely, it is proved that ΩSp5 = Z2 , ΩSp6 = Z2 and ΩSp7 = 0. The indicated values of the groups of cobordisms for dimensions 5 and 6 are known and follow from arguments of the Adams spectral sequence for Sp-cobordisms. The new result is the fact that the seventh group of cobordisms equals 0. This is the fundamental result of the article. The theorem concerning the reconstruction of manifolds with a quasisymplectic structure in the normal bundle, which is proved in the article, and the theorem on integer values of Atiyah-Hirzebruch constitute the basis for the proof. Bibliography: 6 entries.

Some Remarks on Symplectic Cobordism

The object of this paper is to study the ring &2sP of cobordism classes of manifolds whose stable normal (or tangent) bundle reduces to the symplectic group (admits the structure of a quaternionic vector bundle). This ring was studied by Novikov [7] who showed that 2sP (g? Z[1] is a polynomial algebra over Z[?i isomorphic to the ring 7s?O (? Z], where 9410 is the oriented cobordism ring. In addition, he examined the ring &2YsP in low dimensions. Using the Adams spectral sequence, Liulevicius [5] has computed the low groups which are: