Celebratio Mathematica

C. C. Moore and C. Schochet: Global analysis on foliated spaces. Mathematical Sciences Research Institute Publications 9. Springer (New York), 1988. With appendices by Moore, Schochet, S. Hurder and Robert J. Zimmer. A second edition was published in 2006. MR 918974 Zbl 0648.58034 book

Claude L. Schochet	Related
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Group representations, ergodic theory, and mathematical physics: A tribute to George W. Mackey. Edited by R. S. Doran, C. C. Moore, and R. J. Zimmer. Contemporary Mathematics 449. 2008. MR 2385373 Zbl 1131.22001 book

George Whitelaw Mackey	Related
Robert Stuart Doran	Related
Robert Jeffrey Zimmer	Related

C. C. Moore: “Virtual groups 45 years later,” pp. 263–300 in Group representations, ergodic theory, and mathematical physics: A tribute to George W. Mackey (New Orleans, 7–8 January 2007). Edited by R. S. Doran, C. C. Moore, and R. J. Zimmer. Contemporary Mathematics 449. American Mathematical Society (Providence, RI), 2008. MR 2391808 Zbl 1158.22004 incollection

In 1961 George Mackey introduced the concept of a virtual group as an equivalence class under similarity of ergodic measured groupoids, and he developed this circle of ideas in subsequent papers in 1963 and 1966. The goal here is first to explain these ideas, place them in a larger context, and then to show how they have influenced and helped to shape developments in four different but related areas of research over the following 45 years. These areas include first the general area and the connections between ergodic group actions, von Neumann algebras, measurable group theory and rigidity theorems. Then we turn to the second area concerning topological groupoids, \( C^* \)-algebras, \( K \)-theory and cyclic homology, or as it is now termed non-commutative geometry. We briefly discuss some aspects of Lie groupoids, and finally we shall turn attention to the fourth area of Borel equivalence relations seen as a part of descriptive set theory. In each case we trace the influence that Mackey’s ideas have had in shaping each of these four areas of research.

George Whitelaw Mackey	Related
Robert Stuart Doran	Related
Robert Jeffrey Zimmer	Related

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Calvin C. Moore

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