# Protected spin characters, link invariants, and q-nonabelianization

### APA

Yan, F. (2020). Protected spin characters, link invariants, and q-nonabelianization. Perimeter Institute. https://pirsa.org/20090012

### MLA

Yan, Fei. Protected spin characters, link invariants, and q-nonabelianization. Perimeter Institute, Sep. 17, 2020, https://pirsa.org/20090012

### BibTex

@misc{ pirsa_PIRSA:20090012, doi = {10.48660/20090012}, url = {https://pirsa.org/20090012}, author = {Yan, Fei}, keywords = {Mathematical physics}, language = {en}, title = {Protected spin characters, link invariants, and q-nonabelianization}, publisher = {Perimeter Institute}, year = {2020}, month = {sep}, note = {PIRSA:20090012 see, \url{https://pirsa.org}} }

Fei Yan Rutgers University

## Abstract

In this talk I will describe a new link "invariant" (with certain wall-crossing properties) for links L in a three-manifold M, where M takes the form of a surface times the real line. This link "invariant" is constructed via a map, called the q-nonabelianization map, from the

gl(N) skein algebra of M to the gl(1) skein algebra of a covering three-manifold M'. In the special case of M=R^3, this map computes well-known link invariants in a new way. As a physical application, the q-nonabelianization map computes protected spin character counting BPS ground states with spin for line defects in 4d N=2 theories of class-S. I will also mention possible extension to more general three-manifolds, as well as further physical applications to class-S theories. This talk is based on joint work with Andrew Neitzke, and ongoing work with Gregory Moore and Andrew Neitzke.