Functional Analysis and Its Applications

, Volume 35, Issue 2, pp 111–123 | Cite as

The Index Locality Principle in Elliptic Theory

  • V. E. Nazaikinskii
  • B. Yu. Sternin


We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov--Lawson, Anghel, Teleman, Booß-Bavnbek–Wojciechowski, et al. as special cases. In conjunction with some additional conditions (like symmetry conditions), this theorem permits computing the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.


Functional Analysis Additional Condition Wide Class Elliptic Operator Symmetry Condition 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • V. E. Nazaikinskii
    • 1
  • B. Yu. Sternin
    • 2
  1. 1.Institute for Problems in MechanicsRussian Academy of SciencesRussia
  2. 2.Moscow State UniversityRussia

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