Elliptic Theory and Noncommutative Geometry pp 153-156 | Cite as

# Index Formula for a Finite Group Г

Chapter

## Abstract

Let Г be a finite group acting topologically freely on a smooth closed manifold The nonlocal equation can be reduced to a system of local equations. To this end, we replace the functions whose components are obtained as shifts of the original functions by the elements of Г.

*M*, and suppose that we are given a nonlocal elliptic operator^{1}$$
A = \sum\limits_{g \in \Gamma } {T\left( g \right)A\left( g \right):C^\infty \left( {M,\mathbb{C}^n } \right) \to C^\infty \left( {M,\mathbb{C}^n } \right).}
$$

$$
Au = f
$$

*u*and*f*by the vector functions$$
U = \left\{ {U_g } \right\}_{g \in \Gamma } ,F = \left\{ {F_g } \right\}_{g \in \Gamma }
$$

$$
U_g = T\left( g \right)u,F_g = T\left( g \right)f
$$

## Keywords

Finite Group Cotangent Bundle Local Equation Chern Character Index Formula
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Birkhäuser Verlag AG 2008