Cobordisms of symplectic and contact manifolds (Q920441)

The author introduces quasisymplectic \((2n+1)\)-dimensional manifolds, and using them he defines the group \({\mathcal B}_{2n}\) of 2n-dimensional symplectic cobordisms and the group \({\mathcal B}^{{\mathbb{Z}}}_{2n}\) of 2n- dimensional integral symplectic cobordisms. (The integral symplectic manifold (B,\(\Omega\)) is such that \(\Omega\) defines an element from \(H^ 2(B,{\mathbb{Z}}).)\) He proves that \({\mathcal B}_ 2={\mathbb{Z}}\oplus {\mathbb{R}}\), and \({\mathcal B}_ 2^{{\mathbb{Z}}}={\mathbb{Z}}\oplus {\mathbb{Z}}\). Further he introduces quasicontact 2n-dimensional manifolds and defines the group \({\mathcal C}_{2n+1}\) of contact cobordisms. The construction, called compact contactization of an integral symplectic structure, enables him to define a homomorphism \(\kappa\) : \({\mathcal B}^{{\mathbb{Z}}}_{2n}\to {\mathcal C}_{2n+1}\). He shows that \(\kappa =0\). In the end the author presents some more special results concerning the standard contact structure on the sphere bundle of the cotangent bundle over a manifold.