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In this chapter, we present some basic subjects on functional analysis and operator algebras that are necessary to introduce the \(L^2\) -Betti numbers of the reduced \(L^2\) -cohomology groups of the universal covering space of a compact manifold.

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\(L^2\) -Betti Number and von Neumann Trace

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  • 发表日期：

    2025年

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  • Tsuyoshi Kato,
  • Nobuhiro Nakamura

摘要

In this chapter, we present some basic subjects on functional analysis and operator algebras that are necessary to introduce the \(L^2\) -Betti numbers of the reduced \(L^2\) -cohomology groups of the universal covering space of a compact manifold.