Yasin Uskuplu, USC

Abstract: The Steenrod squares are the cohomology operations characterized by a set of axioms including the Cartan relation. These operations define the “Steenrod square” which is an enhancement of the classical cup product and satisfies the Cartan relation. In this talk, I will introduce quantum versions of the Steenrod squares and the Cartan relation. Similarly, these operations define the quantum version of the “Steenrod square” which is an enhancement of the quantum cup product defined on the quantum cohomology of closed monotone symplectic manifolds. By giving some computational examples for the n-dimensional complex projective space, we will see that we need some quantum error terms / quantum deformations leading us to have a correct quantum version of the Cartan relation. These computational results will imply that similar approaches also apply to Fano toric manifolds.