Dual Feynman transform for modular operads

• DOI: 10.4310/cntp.2007.v1.n4.a1
• Publication Date: 2013-08-30T22:59:03Z
• Authors: J. Chuang; A. Lazarev
• Keywords: Dual graph; Contractible space

We introduce and study the notion of a dual Feynman transform smodular operad.This generalizes gives conceptual explanation Kontsevich's construction producing graph cohomology classes from contractible differential graded Frobenius algebra.The modular operad is indeed linear to introduced by Getzler Kapranov when evaluated on vacuum graphs.In marked contrast transform, admits an extremely simple presentation via generators relations; this leads explicit easy description its algebras.We discuss further generalization whose algebras are not necessarily contractible.This naturally rise two-colored complex analogous Boardman-Vogt topological tree complex.