# Infinitary braid groups

## TL;DR

This paper explores the properties of infinitary braid groups, extending the concept of finite braid groups to infinitely many strings, particularly focusing on countable cases.

## Contribution

It introduces and investigates the properties of more complex, infinitely many-string braid groups beyond the traditional finite cases.

## Key findings

- Basic properties of countable infinitary braid groups analyzed
- Extension of braid group concepts to infinite string scenarios
- Foundations for further research on infinite braid structures

## Abstract

An infinitary version of braid groups has been considered as a direct limit of n-braid groups. However, we can imagine more complicated braids with infinitely many strings. We invetisgate basic properties especially when the number of strings is countable.