Equivariant deformation problems and homotopy operators

TL;DR

This paper introduces a method using homotopy operators for $L_$-algebras to parametrize equivariant deformation spaces, providing new proofs of rigidity and unobstructedness.

Contribution

It offers a novel approach to deformation problems via homotopy operators, with explicit algebraic proofs of key theorems.

Findings

Provides a smooth parametrization of deformation spaces.

Establishes new algebraic proofs of rigidity.

Demonstrates unobstructedness in specific cases.

Abstract

We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and explicit proofs of rigidity and unobstructedness theorems.