Duality for arithmetic Dijkgraaf-Witten theory

Naidu classified pairs of finite groups and 3-cocycles that lead to equivalent Dijkgraaf-Witten theories for 3-manifolds. We establish analogous equivalences for arithmetic Dijkgraaf-Witten theory over totally imaginary number fields F containing n-th roots of unity, where n is invertible on X ⊆ spec O_F. Equivalences can fail for the invariant associated to the full ring of integers X = spec O_F.

Get started

Install Nix and enter the development environment with nix develop. Optionally install direnv to automatically enter the development environment.

Thesis

Compile the Typst documents with:

typst compile src/thesis.typ thesis.pdf
typst compile src/paper.typ paper.pdf
typst compile src/talk.typ talk.pdf

Examples

Compare with section 7.2 of thesis.pdf.

Run random samples with Julia:

julia -p auto -e "@everywhere using ArithmeticDijkgraafWitten; dijkgraaf_witten_sample(150, 3, 5)"

Run a specific example:

julia -e "using ArithmeticDijkgraafWitten; @show dijkgraaf_witten([5, 13, -7])"

Run tests:

julia -e "using Pkg; Pkg.test()"

License

Licensed under the MIT License.