In this paper, we build properly embedded singly periodic minimal
surfaces which have infinite total curvature in the quotient
by their period. These surfaces are constructed by adding a handle
to the toroidal half-plane layers defined by H. Karcher. The
technics that we use are to solve a Jenkins-Serrin problem over a
strip domain and to consider the conjugate minimal surface to the
graph. To construct the Jenkins Serrin graph, we solve in fact the
maximal surface equation and use an other conjugation technic.