GKMtools.jl

A Julia package for GKM spaces and their equivariant Gromov–Witten theory.

This Julia package is work in progress. It offers support for calculations involving GKM spaces, including their equivariant Gromov–Witten invariants.

It comes with the supporting article "Computations in equivariant Gromov–Witten theory of GKM spaces" by Daniel Holmes and Giosuè Muratore [HM25].

The package is divided into two parts. The first one deals with foundational material on GKM spaces, including smooth and orbifold GKM graphs, equivariant cohomology, and equivariant vector bundles. The second part, which is currently being adapted to the new implementation, is dedicated to equivariant Gromov–Witten theory.

Installation

This package depends on Oscar, so make sure that Oscar is installed and runs correctly on your system (see the installation instructions). Important: GKMtools.jl must be installed in the same environment where Oscar is available. For example, if Oscar is installed inside WSL on Microsoft Windows, then GKMtools.jl must also be installed and run within that same WSL distribution.

To install the latest release of this package, run:

julia> using Pkg
julia> Pkg.add(url="https://github.com/mgemath/GKMtools.jl", rev="v1.0.0")

This package had a substantial remake. To install the latest legacy version (versions v0.X.X), use:

julia> using Pkg
julia> Pkg.add(url="https://github.com/mgemath/GKMtools.jl", rev="v0.18.2")

The documentation of that legacy version is available here.

Once installed, load the package alongside Oscar with:

julia> using Oscar, GKMtools

AI disclosure

GKMtools was originally written without the use of any AI tools. Starting from version 1.0.0, the authors used Codex (version 6-Astra) and Claude for improving the existing package. Some of the functionalities not present in versions 0.X.X were added with the support of AI, but the general architecture and choice of algorithms are due to the authors. The code was carefully checked and tested by the authors.