A splitting formula in instanton Floer homology

Abstract

In a recent paper, Lin, Ruberman and Saveliev proved a splitting formula expressing the Seiberg-Witten invariant λ S W ( X ) \lambda _{SW}(X) of a smooth 4 4 -manifold with rational homology of S 1 × S 3 S^1\times S^3 in terms of the Frøyshov invariant h ( X ) h(X) and a Lefschetz number in reduced monopole Floer homology. In this note we observe that a similar splitting formula holds in reduced instanton Floer homology.