arXiv subjects

Adam Rennie

Publications and source records attributed to Adam Rennie.

56 records · Page 4Linked to original sources

arXiv2004

The Local Index Formula in Semifinite von Neumann Algebras II: The Even Case

We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean-Singer formula.

math.OA↗

arXiv2001

Poincare Duality and Spin^c Structures for Noncommutative Manifolds

We prove a noncompact Serre-Swan theorem characterising modules which are sections of vector bundles not necessarily trivial at infinity. We then identify the endomorphism algebras of the resulting modules. The endomorphism results continue to hold for the generalisation of these modules to noncommutative, nonunital algebras. Finally, we apply these results to not necessarily compact noncommutative spin manifolds, proving that Poincare Duality implies the Morita equivalence of the `algebra of functions' and the `Clifford algebra.'

math-ph↗