Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-09-12
Internat. Math. Research Notices (1995) 141-153
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, Preprint, Max-Planck-Institut in Bonn
Scientific paper
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 K\"{a}hler manifold $X$, thereby yielding the most general type of homotopy G-algebra 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 sigma-model, the construction of Gromov-Witten invariants in Kontsevich's version.
Gerstenhaber Murray
Voronov Alexander A.
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