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32 results

Page 1 of 2

  • 6 - Localisation Algebras and K-homology
  • from Part Two - Roe Algebras, Localisation Algebras and Assembly
  • Rufus Willett, University of Hawaii, Manoa, Guoliang Yu, Texas A & M University
  • Book: Higher Index Theory
  • Published online: 11 June 2020
  • Print publication: 02 July 2020, pp 217-273
  • View extract

    Summary

    Introduction to assembly as a 'forget control' map from K-homology to K-theory of Roe algebras. Introduction of the Baum-Connes and coarse Baum-Connes conjectures as universal assembly maps. Concrete models for the Baum-Connes conjecture for special cases, and proof of the coarse Baum-Connes conjecture for Euclidean space.

  • 5 - Roe Algebras
  • from Part Two - Roe Algebras, Localisation Algebras and Assembly
  • Rufus Willett, University of Hawaii, Manoa, Guoliang Yu, Texas A & M University
  • Book: Higher Index Theory
  • Published online: 11 June 2020
  • Print publication: 02 July 2020, pp 198-216
  • View extract

    Summary

    Introduction of localisation algebras, and use of these to build an analytic model for K-homology, including a proof that this model is a generalised homology theory. Equivariant versions, and relationships to other models of K-homology.

  • 9 - Products and Poincaré Duality
  • from Part Three - Differential Operators
  • Rufus Willett, University of Hawaii, Manoa, Guoliang Yu, Texas A & M University
  • Book: Higher Index Theory
  • Published online: 11 June 2020
  • Print publication: 02 July 2020, pp 353-392
  • View extract

    Summary

    Applications of assembly maps to the Kadison-Kaplansky conjecture on the existence of idempotents in group algebras, to the existence and study of positive scalar curvature metrics, and to the Novikov conjecture in manifold topology. Historical motivation and some overview of the literature.

Page 1 of 2