Paper's Title:

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

Author(s):

Atefeh Hasan-Zadeh and Hamid-Reza Fanai

DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
E-mail: hasanzadeh.a@ut.ac.ir

Department of Mathematical Sciences,
Sharif University of Technology,
Iran
E-mail: fanai@sharif.edu

Abstract:

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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