## Tokyo Journal of Mathematics

### Some Remarks on the Coarse Index Theorem for Complete Riemannian Manifolds

Shingo KAMIMURA

#### Abstract

In this paper, we state two results on the coarse index for simple models of the coarse geometry. The first one is a coarse index theorem on trivial bundles over even dimensional closed Riemannian manifolds. It comes from the Poincar\'e duals for these base manifold in the trivial bundles. We next show some correspondence between the generator of the coarse cohomology of $\mathbf{R}^n$ and the Riesz transformation on $\mathbf{R}^n$.

#### Article information

Source
Tokyo J. Math., Volume 26, Number 2 (2003), 329-345.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208594

Digital Object Identifier
doi:10.3836/tjm/1244208594

Mathematical Reviews number (MathSciNet)
MR2020789

Zentralblatt MATH identifier
1053.58009

#### Citation

KAMIMURA, Shingo. Some Remarks on the Coarse Index Theorem for Complete Riemannian Manifolds. Tokyo J. Math. 26 (2003), no. 2, 329--345. doi:10.3836/tjm/1244208594. https://projecteuclid.org/euclid.tjm/1244208594

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