# An explicit symmetric DGLA model of a bi-gon

## TL;DR

This paper presents explicit symmetric differential graded Lie algebra (DGLA) models for a bi-gon, extending previous models of the interval to more complex shapes with symmetry considerations.

## Contribution

It provides explicit formulas for a symmetric DGLA model of the bi-gon, incorporating geometric symmetries and advanced structural insights.

## Key findings

- Explicit symmetric DGLA model of the bi-gon is constructed.
- The model extends the work on the DGLA of the interval.
- Uses deeper structural understanding and localizations for non-simply connected spaces.

## Abstract

We give explicit formulae for a DGLA model of the bi-gon which is symmetric under the geometric symmetries of the cell. This follows the work of Lawrence-Sullivan on the (unique) DGLA model of the interval and its construction uses deeper knowledge of the structure of such models and their localisations for non-simply connected spaces.