TY  - BOOK
AU  - Carey,A.L.
AU  - Gayral,V.
AU  - Rennie,A.
AU  - Sukochev,F.A.
TI  - Index theory for locally compact noncommutative geometries
T2  - Memoirs of the American Mathematical Society
SN  - 9780821898383 (pbk. : acidfree paper)
U1  - 510 23
PY  - 2014///
CY  - Providence
PB  - American Mathematical Society
KW  - Index theory (Mathematics)
KW  - Geometry
KW  - Noncommutative algebras
N1  - "Volume 231, number 1085 (second of 5 numbers), September 2014."; Includes bibliographical references (pages 125-127) and index; Introduction--
1. Pseudodifferential calculus and summability--
2. Index pairings for semifinite spectral triples--
3. The local index formula for semifinite spectral triples-- 
4. Applications to index theorems on open manifolds--
5. Noncommutative examples--

Appendix A. Estimates and technical lemmas--
Bibliography--
Index
N2  - In the present text, it is proved that local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new
ER  -