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The bordism group of unbounded KK-cycles

R.J. Deeley ; Magnus Goffeng (Institutionen för matematiska vetenskaper) ; B. MESLAND
Journal of Topology and Analysis (1793-5253). p. 1-46. (2016)
[Artikel, refereegranskad vetenskaplig]

© 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.

Nyckelord: bordism theory , geometric (Formula presented.)-homology , noncommutative geometry , operator algebras , Unbounded (Formula presented.)-theory



Denna post skapades 2017-12-28.
CPL Pubid: 254152

 

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