Oriented Cohomology Rings of the Semisimple Linear Algebraic Groups of Ranks 1 and 2 - Gandhi, Raj (Université d'Ottawa / University of Ottawa, 2021)
In this thesis, we compute minimal presentations in terms of generators and relations for the oriented cohomology rings of several semisimple linear algebraic groups of ranks 1 and 2 over algebraically closed fields of characteristic 0. The main tools we use in this thesis are the combinatorics of Coxeter groups and formal group laws, and recent results of Calm\`es, Gille, Petrov, Zainoulline, and Zhong, which relate the oriented cohomology rings of flag varieties and semisimple linear algebraic groups to the dual of the formal affine Demazure algebra.
Keywords: Algebraic groups; Algebraic geometry; Algebraic oriented cohomology theories; Demazure operator; Formal group law