Manfred Salmhofer, Christian Wieczerkowski Construction of the Renormalized Gross-Neveu Trajectory in $2-\epsilon$ Dimensions (56K, LaTeX2e) ABSTRACT. We construct the renormalized Gross-Neveu trajectory in $2-\epsilon$ dimensions. Our construction uses a contraction mapping for an extended renormalization group. The extension is a running coupling with linear step $\beta$-function. The contraction mapping relies on norm estimates for a fermionic momentum space renormalization group.