On the moduli of periodic instantons (Q1345353)

The manifold \(S^1 \times \mathbb{R}^3\) is end periodic, i.e. may be expressed as a countable union of mutually diffeomorphic manifolds with two ends in which one end of each is identified with the other end of the next and the remaining end of the first is identified with the end of a manifold with a single end. This periodicity allows a certain periodicity in geometric objects on the manifold. In particular there is the set \(\mathcal E\) of asymptotically periodic metrics. It is shown that for a Baire set of \(\varphi \in {\mathcal E}\) the corresponding moduli space is a smooth manifold of identified dimension.