Date of Award
Summer 2019
Document Type
Open Access Thesis
Department
Mathematics
First Advisor
Matthew Ballard
Abstract
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.
Recommended Citation
Otis, J.(2019). An Implementation of the Kapustin-Li Formula. (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/5458