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The purpose of this chapter is to present basic ideas and motivations for the proofs of the Farrell-Jones Conjecture and some information about their long history without getting lost in technical details. So it will be a soft introduction to the methods of proofs conveying only ideas. Moreover, we also want to provide some insight into why some input such as controlled topology, transfers, and flows occurs, which one might not expect at first glance since so far the assembly maps have been purely homotopy theoretic notions. We refer the interested reader, who wants to see more details, to Chapters 21, 22, 23, and 24.

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Motivation, Summary, and History of the Proofs of the Farrell-Jones Conjecture

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  • 发表日期：

    2025年

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  • Wolfgang Lück

摘要

The purpose of this chapter is to present basic ideas and motivations for the proofs of the Farrell-Jones Conjecture and some information about their long history without getting lost in technical details. So it will be a soft introduction to the methods of proofs conveying only ideas. Moreover, we also want to provide some insight into why some input such as controlled topology, transfers, and flows occurs, which one might not expect at first glance since so far the assembly maps have been purely homotopy theoretic notions. We refer the interested reader, who wants to see more details, to Chapters 21, 22, 23, and 24.