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Article Dans Une Revue Comptes Rendus Mathématiques, Rep. Acad. Sci. Canada Année : 2011

On Coarse Spectral Geometry in Even Dimension

Robert Yuncken
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Résumé

Let $\sigma$ be the involution of the Roe algebra $C^*|R|$ which is induced from the reflection $R \to R; x \mapsto -x$. A graded Fredholm module over a separable C∗-algebra A gives rise to a homomorphism $\tilde{\rho}:A \to C^*|R|^\sigma$ to the fixed-point subalgebra. We use this observation to give an even-dimensional analogue of a result of Roe. Namely, we show that the K-theory of this symmetric Roe algebra is $K_0(C^*|R|^\sigma)\cong Z$, $K_1(C^*|R|)=0$, and that the induced map $\tilde{\rho}_*:K_0(A) \to Z$ on K-theory gives the index pairing of K-homology with K-theory.
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Dates et versions

hal-01271779 , version 1 (09-02-2016)

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  • HAL Id : hal-01271779 , version 1

Citer

Robert Yuncken. On Coarse Spectral Geometry in Even Dimension. Comptes Rendus Mathématiques, Rep. Acad. Sci. Canada, 2011, 33 (2), pp.8. ⟨hal-01271779⟩
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