Stably exotic 4-manifolds

Abstract

A pair of closed, smooth $4$-manifolds $M$ and $M'$ are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with copies of $S^2 \times S^2$. Orientable stable exotica do not exist by a result of Gompf, but Kreck showed that nonorientable examples are plentiful. We investigate which values of the fundamental group $π$ and the first and second Stiefel-Whitney classes $w_1$ and $w_2$ admit stably exotic pairs, providing a complete description if $H_5(π;\mathbb{Z})=0$. In particular we produce new stable exotica, and new settings in which they do not arise.

Theorems & Definitions (71)

• Theorem : Gompf Gompf84
• Remark 1.1
• Theorem : Kreck Kreck84*Theorem 1
• Theorem A
• Remark 1.3
• Corollary 1.4
• proof
• Theorem B
• Remark 1.5
• Remark 1.6