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

摘要

We construct an obstruction to the existence of embeddings of a homology 3-sphere into a homology S-3 x S-1 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 S-3 x S-1 and the instantons on it. (C) 2018 Elsevier B.V. All rights reserved.