On a DGL-map between derivations of Sullivan minimal models

Abstract

For a map f:Xrightarrow Y, there is the relative model M(Y)=(Lambda V,d)rightarrow (Lambda Votimes Lambda W,D)simeq M(X) by Sullivan model theory (Félix et al., Rational homotopy theory, graduate texts in mathematics, Springer, Berlin, 2007). Let mathrm{Baut}_1X be the Dold–Lashof classifying space of orientable fibrations with fiber X (Dold and Lashof, Ill J Math 3:285–305, 1959]). Its DGL (differential graded Lie algebra)-model is given by the derivations mathrm{Der}M(X) of the Sullivan minimal model M(X) of X. Then we consider the condition that the restriction b_f:mathrm{Der} (Lambda Votimes Lambda W,D)rightarrow mathrm{Der}(Lambda V,d) is a DGL-map and the related topics.