Relative Solidity results and their applications to rigidity and computations of II_1 factors invariants

Niki Amaraweera Kalutotage; Department of Mathematics, University of Iowa

In this talk, I will present our results on relative solidity for von Neumann algebras of relative hyperbolic groups, which were proved using an interplay between deformation/rigidity and geometric group theory. These findings validate Ozwa's well-known relative solidity conjecture for hyperbolic groups relative to exact and residually finite peripheral subgroups. Our results will apply to significant classes of relatively hyperbolic groups. Using these solidity results, we address the primeness question: "If group G is nonelementary relatively hyperbolic, then the corresponding group von Neumann Algebra L(G) is s-prime."  These structural results were also used to compute canonical invariants such as fundamental groups and one-sided fundamental semigroups. Computations of these invariants play a crucial role in classifying von Neumann Algebras and provide more insight into their structural properties.