The Surgery Exact Triangle in Monopole Floer Homology with Z[i] Coefficients

Abstract

In their seminal paper, Kronheimer, Mrowka, Ozsváth and Szabó, establish the existence of a surgery exact triangle for Monopole Floer homology. The triangle was a theoretical breakthrough and allowed us to answer questions about the surgery correspondence between knots and 3-manifolds that were previously mysterious. A serious limitation of their triangle was that it only holds over characteristic two. In this paper, we establish the existence of a surgery exact triangle using local coefficients valued in Z[i].