New moduli spaces of pointed curves and pencils of flat connections

dc.creatorLosev, A.
dc.creatorManin, Yu.
dc.date2000-01-01
dc.date2000-03-20
dc.date.accessioned2026-07-07T04:33:10Z
dc.date.available2026-07-07T04:33:10Z
dc.descriptionIt is well known that formal solutions to the Associativity Equations are the same as cyclic algebras over the homology operad $(H_*(\bar{M}_{0,n+1}))$ of the moduli spaces of $n$--pointed stable curves of genus zero. In this paper we establish a similar relationship between the pencils of formal flat connections (or solutions to the Commutativity Equations) and homology of a new series $\bar{L}_n$ of pointed stable curves of genus zero. Whereas $\bar{M}_{0,n+1}$ parametrizes trees of $\bold{P}^1$'s with pairwise distinct nonsingular marked points, $\bar{L}_n$ parametrizes strings of $\bold{P}^1$'s stabilized by marked points of two types. The union of all $\bar{L}_n$'s forms a semigroup rather than operad, and the role of operadic algebras is taken over by the representations of the appropriately twisted homology algebra of this union.
dc.description37 pages, AMSTex. Several typos corrected, a reference added, subsection 3.2.2 revised, subsection 3.2.4 added
dc.identifierhttps://arxiv.org/abs/math/0001003
dc.identifierhttp://arxiv.org/abs/math/0001003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58473
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleNew moduli spaces of pointed curves and pencils of flat connections
dc.typetext

Files

Collections