Journal article, 2016

© 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.

bordism theory

noncommutative geometry

operator algebras

Unbounded (Formula presented.)-theory

geometric (Formula presented.)-homology

University of Gothenburg

Chalmers, Mathematical Sciences

1793-5253 (ISSN) 1793-7167 (eISSN)

1-46Basic sciences

Geometry

Mathematical Analysis

10.1142/S1793525318500012