Compactified configuration space of points on a line and homotopies of $A_{\infty }$ morphisms

Abstract

We construct a configuration space model for a particular 2-colored differential graded operad encoding the structure of two $A_{\infty }$ algebras with two $A_{\infty }$ morphisms and a homotopy between the morphisms. The cohomology of this operad is shown to be the well-known 2-colored operad encoding the structure of two associative algebras and of an associative algebra morphism between them.

18 pages

References in corpus (2)

• Deformation theory of representations of prop(erad)s
• Coloured Koszul duality and strongly homotopy operads