1,588 research outputs found
Grothendieck-Teichmueller group, operads and graph complexes: a survey
This paper attempts to provide a more or less self-contained introduction
into theory of the Grothendieck-Teichmueller group and Drinfeld associators
using the theory of operads and graph complexes.Comment: One reference is adde
Operads, configuration spaces and quantization
We review several well-known operads of compactified configuration spaces and
construct several new such operads, C, in the category of smooth manifolds with
corners whose complexes of fundamental chains give us (i) the 2-coloured operad
of A-infinity algebras and their homotopy morphisms, (ii) the 2-coloured operad
of L-infinity algebras and their homotopy morphisms, and (iii) the 4-coloured
operad of open-closed homotopy algebras and their homotopy morphisms. Two
gadgets - a (coloured) operad of Feynman graphs and a de Rham field theory on C
- are introduced and used to construct quantized representations of the
(fundamental) chain operad of C which are given by Feynman type sums over
graphs and depend on choices of propagators.Comment: 58 page
The extended moduli space of special Lagrangian submanifolds
It is well known that the moduli space of all deformations of a compact
special Lagrangian submanifold in a Calabi-Yau manifold within the
class of special Lagrangian submanifolds is isomorphic to the first de Rham
cohomology group of . Reinterpreting the embedding data within
the mathematical framework of the Batalin-Vilkovisky quantization, we find a
natural deformation problem which extends the above moduli space to the full de
Rham cohomology group of .Comment: 15pages. A new citation and a correctio
Geometry of Kodaira moduli spaces
A general theorem on the existence of natural torsion-free affine connections
on a complete family of compact complex submanifolds in a complex manifold is
proved. Applications to twistor theory are discussed.Comment: 10 pages, LaTe
Strong homotopy properads
In this paper we prove that the structure of strong homotopy properad
transfers over left homotopy inverses and give explicit formulae for the
induced structure.Comment: Final version, 19 page
- …