The bordism group of unbounded KK-cycles

© 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.

Goffeng, Magnus C H T,1987Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)goffeng (författare)
Mesland, BramUniversiteit Leiden (UL),Leiden University (UL) (författare)
University of Colorado at BoulderInstitutionen för matematiska vetenskaper (creator_code:org_t)

Av författaren/redakt...: Deeley, Robin J.; Goffeng, Magnus ...; Mesland, Bram

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