Homotopy Galgebras and moduli space operad
Abstract
This paper reemphasizes 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 G (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 Galgebra structure on $\Omega^\bullet X$. One of the reasons to put this operadic nonsense on the physics bulletin board is that we use a typical construction of supersymmetric sigmamodel, the construction of GromovWitten invariants in Kontsevich's version.
 Publication:

arXiv eprints
 Pub Date:
 September 1994
 DOI:
 10.48550/arXiv.hepth/9409063
 arXiv:
 arXiv:hepth/9409063
 Bibcode:
 1994hep.th....9063G
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Differential Geometry
 EPrint:
 12 pages, Preprint, MaxPlanckInstitut in Bonn