Cap-product structures on the Fintushel–Stern spectral sequence

Abstract

We show that there is a well-defined cap-product structure on the Fintushel–Stern spectral sequence and the induced cap-product structure on the ℤ8-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological point of view, which multiplies a finite-dimensional cohomlogy class by an infinite-dimensional homology class (Floer cycles) to get another infinite-dimensional homology class.