Contact surgery and symplectic handlebodies
\textit{C. Meckert} [Ann. Inst. Fourier 32, No. 3, 251-260 (1982; Zbl 0471.58001)] has shown that the connected sum of two contact manifolds has a contact structure. The author of the paper extends Meckert's result as follows. Let \(Y\) be any isotropic sphere in a contact manifold \(X\), with a trivialization of the conformal symplectic normal bundle of \(Y\) (the conformal symplectic normal bundle is a direct summand of the ordinary normal bundle of \(Y\) in \(X\)). Then the manifold \(X'\) obtained from \(X\) by elementary surgery along \(Y\) (using the framing induced by the trivialization) has a contact structure. Moreover, \(X\) and \(X'\) both form the boundary of an elementary cobordism \(P\) having a symplectic structure together with a conformally symplectic vector field which is transverse to the boundary and which actually produces the original contact structure on \(X\) and the contact structure on \(X'\).
elementary cobordism having a symplectic structure
scientific article; zbMATH DE number 11093