# Twisting Elements in Homotopy G-algebras - Mathematics > Algebraic Topology

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Abstract: We study the notion of twisting elements $da=a\cup 1a$ with respect to$\cup 1$ product when it is a part of homotopy Gerstenhaber algebra structure.This allows to bring to one context the two classical concepts, the theory ofdeformation of algebras of M. Gerstenhaber, and $A\infty$-algebras of J.Stasheff.