Nonuniform hyperbolic lattices and exotic smooth structures
This paper considers the operation of a manifold \(M^ n\) of removing a tube \(S^ 1\times D^{n-1}\) and reinserting it with a twist along the boundary. It is used to change the differentiable structure of the manifold, even when \(M\) is noncompact. The standard technique for changing the differentiable structure of \(M\) is to form the connected sum \(M\# \Sigma\), where \(\Sigma\) is a homotopy sphere. There are, however, cases in which this connected sum method does not work (when \(M\) is noncompact, for example) and the new method works.
scientific article; zbMATH DE number 488224