Instantons for 4-manifolds with periodic ends and an obstruction to embeddings of 3-manifolds

We construct an obstruction to the existence of embeddings of a homology 3-sphere into a homology S3×S1 under some cohomological condition. The obstruction is defined as an element in the filtered version of the instanton Floer cohomology due to Fintushel and Stern. We make use of the Z-fold covering space of homology S3×S1 and the instantons on it.