756 research outputs found
Extended modular operad
This paper is a sequel to [LoMa] where moduli spaces of painted stable curves
were introduced and studied. We define the extended modular operad of genus
zero, algebras over this operad, and study the formal differential geometric
structures related to these algebras: pencils of flat connections and Frobenius
manifolds without metric. We focus here on the combinatorial aspects of the
picture. Algebraic geometric aspects are treated in [Ma2].Comment: 38 pp., amstex file, no figures. This version contains additional
references and minor change
Morpho-logical Investigations: Wittgenstein and Spengler
The influence of Spengler on Wittgenstein's philosophical development is considered. The point of interest is in a significant methodological restructuring which it appears to have produced. After an initial over-enthusiastic reception, Wittgenstein is seen to object on some points which he attempted to emend in his own philosophy. Spengler's name disappeared inreworked manuscripts but traces persist in the
Philosophical Investigations and an important section (§89-133) is found to be connected with it
New moduli spaces of pointed curves and pencils of flat connections
It is well known that formal solutions to the Associativity Equations are the
same as cyclic algebras over the homology operad of
the moduli spaces of --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
of pointed stable curves of genus zero. Whereas
parametrizes trees of 's with pairwise distinct nonsingular marked
points, parametrizes strings of 's stabilized by marked
points of two types. The union of all '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.Comment: 37 pages, AMSTex. Several typos corrected, a reference added,
subsection 3.2.2 revised, subsection 3.2.4 adde
On Connection between Topological Landau-Ginzburg Gravity and Integrable Systems
We study flows on the space of topological Landau-Ginzburg theories coupled
to topological gravity. We argue that flows corresponding to gravitational
descendants change the target space from a complex plane to a punctured complex
plane and lead to the motion of punctures.It is shown that the evolution of the
topological theory due to these flows is given by dispersionless limit of KP
hierarchy. We argue that the generating function of correlators in such
theories are equal to the logarithm of the tau-function of Generalized
Kontsevich Model.Comment: 17 p. late
Anticommutativity Equation in Topological Quantum Mechanics
We consider topological quantum mechanics as an example of topological field
theory and show that its special properties lead to numerous interesting
relations for topological corellators in this theory. We prove that the
generating function for thus corellators satisfies the
anticommutativity equation . We show that the
commutativity equation could be considered as a special case of the
anticommutativity equation.Comment: 6 pages, no figures, Late
On the Length of the Relaxation Zone of Ionization Behind a Strong Shock Wave Front in the Air
Relaxation zone behind strong shock wave front in ai
- …