Date of Award
Open Access Thesis
Let R be a regular local ring and take ! to be an isolated singularity on R. Taking Z/2-graded R-modules, X and Y , a matrix factorization of ω is a pair of morphisms (ϕ, ψ) such that ϕ⃝◦ψ = ω and ψ⃝◦ϕ = ω are satisfied in the diagram X ϕ → Y ψ→ X. We will discuss the category of matrix factorizations of ! in R and lead into the homotopy category of matrix factorizations as well as its historical development. Finally, we will conclude with the statement of the Kapustin-Li formula for the duality pairing on the morphisms in the matrix factorization category of (R, ω) and discuss its implementation in SageMath.
Otis, J.(2019). An Implementation of the Kapustin-Li Formula. (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/5458