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Explore the intricate connections between geometry and arithmeticity of hyperbolic orbifolds and manifolds in this 59-minute lecture by Nikolay Bogachev. Delve into the concept of fc-subspaces, which correspond to finite symmetries of finite covers or fixed point sets of finite subgroups of the commensurator. Discover a new arithmeticity criterion for hyperbolic orbifolds based on the presence of infinitely many fc-subspaces. Examine the relationship between immersed totally geodesic suborbifolds and fc-subspaces in arithmetic hyperbolic orbifolds. Learn about examples of non-arithmetic orbifolds containing non-fc subspaces of codimension one. Gain insights into the algebraic characterization of immersions of arithmetic hyperbolic orbifolds and its application to detecting arithmeticity of hyperbolic n-manifolds. If time allows, explore applications of fc-subspaces to reflection groups and hyperbolic link complements based on upcoming research.
