Sutured monopole Floer homology (SHM) and sutured Instanton Floer homology (SHI) were introduced by Kronheimer and Mrowka. They also constructed knot Floer homologies by taking the SHM or SHI of the knot complements with meridional sutures. These knot Floer homologies are the counterpart in monopole and instanton theories to HFK-hat in Heegaard Floer theory. In this talk, we will make use of other sutures on the boundary of knot complements and introduce new versions of knot Floer Homology in monopole and instanton theories, called KHM-minus and KHI-minus,  which closely resemble HFK-minus in Heegaard Floer theory.

We will present the construction as well as proving some basic properties. Based on this minus version, we can also define a tau invariant in monopole and instanton theory and prove its concordance invariance. If time permits, we will also present the computations for some special knots.