861 research outputs found
On Coarse Spectral Geometry in Even Dimension
Let be the involution of the Roe algebra \Roe{\RR} which is
induced from the reflection \RR\to\RR; x\mapsto -x. A graded Fredholm module
over a separable -algebra gives rise to a homomorphism
\tilde{\rho}:A\to\Roe{\RR}^\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 -theory of this symmetric Roe algebra is
K_0(\Roe{\RR}^\sigma)\cong\ZZ, K_1(\Roe{\RR})=0, and that the induced map
\tilde{\rho}_*:K_0(A) \to \ZZ on -theory gives the index pairing of
-homology with -theory
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