arXiv subjects

Jan-Luca Spellmann

Publications and source records attributed to Jan-Luca Spellmann.

2 recordsLinked to original sources

arXiv2023

Renormalized Reshetikhin-Turaev invariants for the unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$

This paper is a self-contained introduction to the theory of renormalized Reshetikhin-Turaev invariants of links defined by Geer, Patureau-Mirand and Turaev. Whereas the standard Reshetikhin-Turaev theory of a $\mathbb{C}$-linear ribbon category assigns the trivial invariant to any link with a component colored by a simple object of vanishing quantum dimension, the renormalized theory does not. We give a streamlined development of the renormalized Reshetikhin-Turaev theory of links for the category of weight modules over the restricted unrolled quantum group of $\mathfrak{sl}_2(\mathbb{C})$ at an even root of unity.

math.QA↗

arXiv2022

Matrix factorizations, Reality and Kn\"orrer periodicity

Motivated by periodicity theorems for Real $K$-theory and Grothendieck--Witt theory and, separately, work of Hori-Walcher on the physics of Landau-Ginzburg orientifolds, we introduce and study categories of Real matrix factorizations. Our main results are generalizations of Kn\"{o}rrer periodicity to categories of Real matrix factorizations. These generalizations are structurally similar to $(1,1)$-periodicity for $KR$-theory and $4$-periodicity for Grothendieck-Witt theory. We use techniques from Real categorical representation theory which allow us to incorporate into our main results equivariance for a finite group and discrete torsion twists.

math.KT↗