Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• ISSN: 1815-0659
• Main Authors: Hablicsek, Márton, Vogel, Jesse
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211809
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories. Márton Hablicsek and Jesse Vogel. SIGMA 18 (2022), 095, 38 pages

In this paper, we use a geometric technique developed by González-Prieto, Logares, Muñoz, and Newstead to study the -representation variety of surface groups G(Σ) of arbitrary genus for being the group of upper triangular matrices of fixed rank. Explicitly, we compute the virtual classes in the Röt...