Twisted Equivariant Matrix Factorizations

Author

Jan-Luca Spellmann, Utah State UniversityFollow

Date of Award:

8-2025

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

Matthew B. Young

Committee

Matthew B. Young

Committee

Nathan Geer

Committee

Peter Crooks

Committee

Zhaohu Nie

Committee

Oscar Varela

Abstract

We introduce and study categories of twisted equivariant matrix factorizations MF^α_G(R, w), which are categories of matrix factorizations of a potential w over the local ring R = C[x₁, . . . , x_n] together with an action by a finite group G that is twisted via a 2-cocycle α. These categories provide rich examples of Z/2Z-differentially graded categories in the context of non-commutative geometry and come up naturally in the study of boundary conditions of 3d Rozansky–Witten theories. We prove that under certain assumptions on (R, w) the categories of twisted matrix factorizations MF^α_G(R, w) are smooth, proper and triangulated. In particular we prove that they are generated by a compact generator. Following Dyckerhoff and Polishchuk–Vaintrob, we compute the Hochschild homology and cohomology of these categories and determine explicitly all ingredients of the categorical Hirzebruch–Riemann–Roch theorem proved in [Shk13].

Checksum

07c55c2b7d61b82280d6291941837c4e

Recommended Citation

Spellmann, Jan-Luca, "Twisted Equivariant Matrix Factorizations" (2025). All Graduate Theses and Dissertations, Fall 2023 to Present. 612.
https://digitalcommons.usu.edu/etd2023/612