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sheaf of L-∞ algebras

Contents

Context

\infty-Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

(,1)(\infty,1)-Topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Idea

A sheaf of L L_\infty-algebras is a suitable sheaf/stack/∞-stack of L-∞ algebras/dg-Lie algebras.

These structures appear in the deformation theory of the given base space/site: where a single L-∞ algebra is equivalently a formal moduli problem (hence “over the point), so a sheaf of these over some base XX may be thought of as an XX-parameterized formal moduli problem (eg. Hinich 03).

References

Discussion in the context of deformation theory/parameterized formal moduli problems is in

Quasi-coherent sheaves of dg-Lie algebras appear in

Discussion in physics, of sheaves of L L_\infty-algebras of physical fields in prequantum field theory includes

Created on January 3, 2014 at 16:24:20. See the history of this page for a list of all contributions to it.