Soumyadip Thandar
TIFR, Mumbai
December 7, 2023
Classifying Equivariant Rational Homotopy Type up to Isomorphic Cohomology Diagram: Algebraic models for rational homotopy theory were developed by Quillen (via differential graded Lie algebra model) and Sullivan (via commutative differential graded algebra model) and the same for equivariant rational homotopy theory were developed by Triantafillou and Scull for finite group actions and S1-action, respectively. They showed that given a diagram of rational cohomology algebras from the orbit category of a group $G$, there is a unique minimal system of DGAs (covariant functors from the orbit category of $G$ to the category of differential graded algebras) and hence a unique equivariant rational homotopy type that is weakly equivalent to it. However, there can be several equivariant rational homotopy types with the same diagram of cohomology algebras. Halperin, Stasheff, and others, studied the problem of classifying rational homotopy types up to cohomology in the non-equivariant case.
TIFR, Mumbai
December 7, 2023
Classifying Equivariant Rational Homotopy Type up to Isomorphic Cohomology Diagram: Algebraic models for rational homotopy theory were developed by Quillen (via differential graded Lie algebra model) and Sullivan (via commutative differential graded algebra model) and the same for equivariant rational homotopy theory were developed by Triantafillou and Scull for finite group actions and S1-action, respectively. They showed that given a diagram of rational cohomology algebras from the orbit category of a group $G$, there is a unique minimal system of DGAs (covariant functors from the orbit category of $G$ to the category of differential graded algebras) and hence a unique equivariant rational homotopy type that is weakly equivalent to it. However, there can be several equivariant rational homotopy types with the same diagram of cohomology algebras. Halperin, Stasheff, and others, studied the problem of classifying rational homotopy types up to cohomology in the non-equivariant case.
In this talk, I will discuss this question in the equivariant case. For the case $G = \mathbb Z_p$ under suitable conditions, the equivariant rational homotopy types with isomorphic diagram of cohomology algebras is determined.