paper

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

arXiv:1707.08555 · doi:10.1016/j.topol.2018.04.016

Abstract

We construct an obstruction for the existence of embeddings of homology $3$ -sphere into homology $S^{3} \times S^{1}$ under some cohomological condition. The obstruction is defined as an element in the filtered version of the instanton Floer cohomology due to R.Fintushel-R.Stern. We make use of the $Z$ -fold covering space of homology $S^{3} \times S^{1}$ and the instantons on it.

34 pages