Nonexistence of twists generating exotic 4-manifolds

Kouichi Yasui

Published 2016-10-13Version 1

It is well known that, for any exotic pair of simply connected closed 4-manifolds, one is obtained by twisting the other along a contractible submanifold. In contrast to this fact, we show that there exists an infinite family of pairwise exotic 4-manifolds such that, for any 4-manifold $X$ and any compact codimension zero submanifold $W$ with $b_1(\partial W)=0$, the family cannot be generated by twisting $X$ along $W$ and varying the gluing map. Furthermore, for any member $X$ and any submanifold $W$ with a certain mild condition, the family cannot be generated from $X$ by removing $W$ and gluing other 4-manifolds. We moreover provide various such families.