Homotopy G-algebras and moduli space operad

Abstract

This paper emphasizes the ubiquitous role of moduli spaces of algebraic curves in associative algebra and algebraic topology. The main results are: (1) the space of an operad with multiplication is a homotopy Gerstenhaber (i.e., homotopy graded Poisson) algebra; (2) the singular cochain complex is naturally an operad; (3) the operad of decorated moduli spaces acts naturally on the de Rham complex ${\Omega }^{\bullet }X$ of a Kähler manifold $X$, thereby yielding the most general type of homotopy G-algebra structure on ${\Omega }^{\bullet }X$.

13 pages, weird symbols caused by an outdated version of LaTeX corrected, references updated, motivation for the sign convention clarified

References in corpus (2)

• Operads, homotopy algebra and iterated integrals for double loop spaces
• On operad structures of moduli spaces and string theory

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