On a DGL-map between derivations of Sullivan minimal models

Abstract

Abstract For a map $$f:X\rightarrow Y$$ f : X → Y , there is the relative model $$M(Y)=(\Lambda V,d)\rightarrow (\Lambda V\otimes \Lambda W,D)\simeq M(X)$$ M ( Y ) = ( Λ V , d ) → ( Λ V ⊗ Λ W , D ) ≃ M ( X ) by Sullivan model theory (Félix et al., Rational homotopy theory, graduate texts in mathematics, Springer, Berlin, 2007). Let $$\mathrm{Baut}_1X$$ Baut 1 X 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 $$\mathrm{Der}M(X)$$ Der M ( X ) of the Sullivan minimal model M(X) of X. Then we consider the condition that the restriction $$b_f:\mathrm{Der} (\Lambda V\otimes \Lambda W,D)\rightarrow \mathrm{Der}(\Lambda V,d) $$ b f : Der ( Λ V ⊗ Λ W , D ) → Der ( Λ V , d ) is a DGL-map and the related topics.

Keywords

• 55P62
• 55R15