标题： 具有预定基本群的奇异非可定向四维流形 显示英文标题

标题： Exotic non-orientable four-manifolds with prescribed fundamental group

摘要： 我们证明，任何具有指数二子群的有限表示群都可以作为闭合光滑非定向四流形的基本群，该流形具有通过执行Gluck扭转得到的奇异光滑结构。这些四流形的方向2覆盖是微分同构的。在添加任意多对2球面的乘积后，这两种光滑结构仍然不等价，而在添加单个复射影平面后则稳定。 显示英文摘要

摘要： We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist. The orientation 2-covers of these four-manifolds are diffeomorphic. These two smooth structures remain inequivalent after adding arbitrarily many copies of the product of a pair of 2-spheres and stabilize after adding a single copy of the complex projective plane.