562 research outputs found
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
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