An explicit L_∞ structure for the components of mapping spaces

摘要

In this paper, we describe an explicit Loo-algebra structure on the differential graded vector space of Lie γ -derivations between two differential graded Lie algebras where the source is minimal free. If γ is a Lie model for a based map between a finite simply connected complex and a nilpotent complex of finite type over Q, then the above L_∞-algebra is a model for the corresponding component of the space of based maps.