Elliptic Theory and Noncommutative Geometry pp 115-125 | Cite as

# Cohomological Formula for the Λ-Index

Chapter

## Abstract

In Chap. 7, we obtained a for nonlocal elliptic operators, where
However, the cohomological formula was obtained only for the usual Fredholm index, which can be extracted from the Λ-Fredholm index by the formula where

*K*-theoretical index formula$$
ind_\Lambda \left( D \right) = p_! \left[ {\sigma \left( D \right)} \right],
$$

- 1.
Λ =

*C**(Г) is the group*C**-algebra of group Г. - 2.
ind

_{Λ}(*D*) ∈*K*_{0}(Λ) is the Λ-Fredholm index of an operator in Hilbert Λ-modules associated with symbol*σ*(*D*) (see Sec. 5.2). - 3.is the direct image mapping corresponding to the projection$$ p_! :K_0 \left( {C_0 \left( {T^ * M} \right) \rtimes \Gamma } \right) \to K_0 \left( \Lambda \right) $$
*p*:*M*→ {*pt*} of the manifold*M*into the one-point space.

$$
indD = \alpha _ * ind_\Lambda \left( D \right),
$$

*α*: Λ → ℂ is the “forgetful” homomorphism associated with the trivial representation of Г in ℂ (see Proposition 5.2).## Keywords

Conjugacy Class Curvature Form Free Abelian Group Leibniz Rule Chern Character
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