Relative solidity results for von Neumann algebras and their applications to W*-rigidity questions and invariant computations

This dissertation mainly investigates Ozawa's relative solidity conjecture for relative hyperbolic groups. In the general theory of relative hyperbolic groups, it is well-known that if a non-elementary group G is hyperbolic relative to a subgroup H, then for any non-amenable commuting subgroups A, B