# braid: Types and functions to work with braids and Khovanov homology.

[ bsd3, library, math, program ] [ Propose Tags ]

A library to work with braids and Khovanov homology. The main focus of the package is computing (the braid invariant kappa)[http://arxiv.org/abs/1507.06263] defined by (the package author)[adamsaltz.com] and (Diana Hubbard)[https://sites.google.com/site/dianadhubbard/]. Braids are encoded by their indexwidth and a word in the standard [Artin generators](https:en.wikipedia.orgwiki/Braid_group#Generators_and_relations). To represent the 4-strand braid sigma_1sigma_2sigma^(-1)_3 use

Braid [1,2,-3] 4

The function computeKappa in the module Kappa returns 'Just kappa' if kappa is finite and Nothing otherwise. More helper functions for working with Khovanov homology and reduced Khovanov homology will be included soon.

The module Braiddiagrams creates diagrams for braids, their closures, and their resolutions. E.g. to dra

The executable KappaView draws the pre-images of the (transverse invariant psi)[http://arxiv.org/abs/math/0412184] with lowest k-grading. The minus-labeled components are indicated by dots.

[Index]