The DGL’s L[sup(k)] and L[sup(k)]

We begin Chapter 2 with a lengthy review of definitions and notations that will serve us throughout the monograph. After this review we define some “altered binomial coeffi­ cients” which are necessary for the construction of a special differential graded Lie algebra denoted (Lk,d ). In Chapter 9 we will identify (ULk,d) as the Adams-Hilton model for the space Fk, but for now we analyze it from a purely algebraic viewpoint. It will be useful to have the properties of (Lk, d) at our fingertips when the times comes to work with its geometric realization. The properties of Lk are inseparable from those of a Lie subalgebra denoted Lk, so we take a hard look at Lk as well. In Chapters 10 and 13 Lk will serve as our guide to the homotopy of the space Ek.