
TL;DR
This paper explores the existence and classification of stably exotic 4-manifolds, which are topologically similar but smoothly distinct after stabilization, focusing on the role of fundamental groups and characteristic classes.
Contribution
It provides a complete classification of stably exotic 4-manifolds based on fundamental groups and Stiefel-Whitney classes, and introduces new examples and non-existence results.
Findings
Nonorientable stable exotica are plentiful, orientable ones do not exist.
Complete classification when $H_5( ext{pi}; extbf{Z})=0$.
New examples of stable exotica and settings where they do not occur.
Abstract
A pair of closed, smooth -manifolds and are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with copies of . 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 and the first and second Stiefel-Whitney classes and admit stably exotic pairs, providing a complete description if . In particular we produce new stable exotica, and new settings in which they do not arise.
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