Assembly maps

  title={Assembly maps},
  author={Wolfgang Lueck},
  journal={Handbook of Homotopy Theory},
  • W. Lueck
  • Published 1 May 2018
  • Mathematics
  • Handbook of Homotopy Theory
We introduce and analyze the concept of an assembly map from the original homotopy theoretic point of view. We give also interpretations in terms of surgery theory, controlled topology and index theory. The motivation is that prominent conjectures of Farrell-Jones and Baum-Connes about K- and L-theory of group rings and group C^*-algebras predict that certain assembly maps are weak homotopy equivalences. 

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