263 research outputs found
Combinatorics and formal geometry of the master equation
We give a general treatment of the master equation in homotopy algebras and
describe the operads and formal differential geometric objects governing the
corresponding algebraic structures. We show that the notion of Maurer-Cartan
twisting is encoded in certain automorphisms of these universal objects
Solving the noncommutative Batalin-Vilkovisky equation
I show that a summation over ribbon graphs with legs gives the construction
of the solutions to the noncommutative Batalin-Vilkovisky equation, including
the equivariant version. This generalizes the known construction of A-infinity
algebra via summation over ribbon trees. These solutions give naturally the
supersymmetric matrix action functionals, which are the gl(N)-equivariantly
closed differential forms on the matrix spaces, which were introduced in one of
my previous papers "Noncommmutative Batalin-Vilkovisky geometry and Matrix
integrals" (arXiv:0912.5484, electronic CNRS preprint
hal-00102085(28/09/2006)).Comment: 17 pages, electronic CNRS preprint hal-00464794 (17/03/2010
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
Relations Among Universal Equations For Gromov-Witten Invariants
In this paper, we study relations among known universal equations for
Gromov-Witten invariants at genus 1 and 2.Comment: LaTex file, 13 page
Two-dimensional topological gravity and equivariant cohomology
In this paper, we examine the analogy between topological string theory and
equivariant cohomology. We also show that the equivariant cohomology of a
topological conformal field theory carries a certain algebraic structure, which
we call a gravity algebra. (Error on page 9 corrected: BRS current contains
total derivatives.)Comment: 18 page
From Zwiebach invariants to Getzler relation
We introduce the notion of Zwiebach invariants that generalize Gromov-Witten
invariants and homotopical algebra structures. We outline the induction
procedure that induces the structure of Zwiebach on the subbicomplex, that
gives the structure of Gromov-Witten invariants on subbicomplex with zero
diffferentials. We propose to treat Hodge dGBV with 1/12 axiom as the simplest
set of Zwiebach invariants, and explicitely prove that it induces WDVV and
Getzler equations in genera 0 and 1 respectively.Comment: 35 page
Matrix De Rham complex and quantum A-infinity algebras
I establish the relation of the non-commutative BV-formalism with
super-invariant matrix integration. In particular, the non-commutative
BV-equation, defining the quantum A-infinity-algebras, introduced in "Modular
operads and Batalin-Vilkovisky geometry" IMRN, Vol. 2007, doi:
10.1093/imrn/rnm075, is represented via de Rham differential acting on the
matrix spaces related with Bernstein-Leites simple associative algebras with
odd trace q(N), and with gl(N|N). I also show that the Lagrangians of the
matrix integrals from "Noncommmutative Batalin-Vilkovisky geometry and Matrix
integrals", Comptes Rendus Mathematique, vol 348 (2010), pp. 359-362,
arXiv:0912.5484, are equivariantly closed differential forms.Comment: published versio
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