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Paper's Title:

Applications of Von Neumann Algebras to Rigidity Problems of (2-Step) Riemannian (Nil-)Manifolds


Atefeh Hasan-Zadeh and Hamid-Reza Fanai

DFouman Faculty of Engineering,
College of Engineering, University of Tehran,

Department of Mathematical Sciences,
Sharif University of Technology,


In this paper, basic notions of von Neumann algebra and its direct analogues in the realm of groupoids and measure spaces have been considered. By recovering the action of a locally compact Lie group from a crossed product of a von Neumann algebra, other proof of one of a geometric propositions of O'Neil and an extension of it has been proposed. Also, using the advanced exploration of nilmanifolds in measure spaces and their corresponding automorphisms (Lie algebraic derivations) a different proof of an analytic theorem of Gordon and Mao has been attained. These two propositions are of the most important ones for rigidity problems of Riemannian manifolds especially 2-step nilmanifolds.

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