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  • Deeley, Robin J., et al. (author)
  • The bordism group of unbounded KK-cycles
  • 2018
  • In: Journal of Topology and Analysis. - 1793-5253 .- 1793-7167. ; 10:2
  • Journal article (peer-reviewed)abstract
    • © 2018 World Scientific Publishing Company We consider Hilsum’s notion of bordism as an equivalence relation on unbounded (Formula presented.)-cycles and study the equivalence classes. Upon fixing two (Formula presented.)-algebras, and a ∗-subalgebra dense in the first (Formula presented.)-algebra, a (Formula presented.)-graded abelian group is obtained; it maps to the Kasparov (Formula presented.)-group of the two (Formula presented.)-algebras via the bounded transform. We study properties of this map both in general and in specific examples. In particular, it is an isomorphism if the first (Formula presented.)-algebra is the complex numbers (i.e. for (Formula presented.)-theory) and is a split surjection if the first (Formula presented.)-algebra is the continuous functions on a compact manifold with boundary when one uses the Lipschitz functions as the dense ∗-subalgebra.
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Type of publication
journal article (1)
Type of content
peer-reviewed (1)
Author/Editor
Goffeng, Magnus C H ... (1)
Deeley, Robin J. (1)
Mesland, Bram (1)
University
University of Gothenburg (1)
Chalmers University of Technology (1)
Language
English (1)
Research subject (UKÄ/SCB)
Natural sciences (1)
Year

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