2024 Theses Doctoral

# Ext Enhanced Soergel Diagrammatics for Dihedral Groups

We compute Ext groups between Soergel Bimodules associated to the infinite/finite dihedral group for a realization in characteristic 0 and show that they are free right 𝖱−modules with an explicit basis. We then give a diagrammatic presentation for the corresponding monoidal category of Ext-enhanced Soergel Bimodules. As applications, we compute reduced triply graded link homology 𝐇̅𝐇̅𝐇̅ of the connect sum of two Hopf links as an 𝖱−module and show that the Poincare series for the Hochschild homology of Soergel Bimodules of finite dihedral type categorifies Gomi's trace for finite dihedral groups.

## Subjects

## Files

- Li_columbia_0054D_18427.pdf application/pdf 819 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Khovanov, Mikhail G.
- Degree
- Ph.D., Columbia University
- Published Here
- September 4, 2024