6 A. L. CAREY, V. GAYRAL, A. RENNIE, and F. A. SUKOCHEV
The applications to the index theory for Dirac-type operators on manifolds of
bounded geometry are contained in Chapter 4. Also in Chapter 4 is a version of the
Atiyah
L2-index
Theorem that applies to covering spaces of noncompact manifolds
of bounded geometry. In Chapter 5 we make a start on noncommutative examples,
looking at torus actions on
C∗-algebras
and at the Moyal plane. Any further
treatment of noncommutative examples would add considerably to the length of
this article, and is best left for another place.
Acknowledgements. This research was supported by the Australian Re-
search Council, the Max Planck Institute for Mathematics (Bonn) and the Banff
International Research Station. A. Carey also thanks the Alexander von Humboldt
Stiftung and colleagues in the University of unster and V. Gayral also thanks the
CNRS and the University of Metz. We would like to thank our colleagues John
Phillips and Magda Georgescu for discussions on nonunital spectral flow. Special
thanks are given to Steven Lord, Roger Senior, Anna Tomskova and Dmitriy Zanin
for careful readings of this manuscript at various stages. We also thank Emmanuel
Pedon for discussions on the Kato inequality, Raimar Wulkenhaar for discussions
on index computations for the Moyal plane, and Gilles Carron, Thierry Coulhon,
Batu uneysu and Yuri Korduykov for discussions related to heat-kernels on non-
compact manifolds. Finally, it is a pleasure to thank the referees: their exceptional
efforts have greatly improved this work.
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