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arXiv · 1901.10419

The principal-symbol index map for an algebra of pseudodifferential operators

Severino T. Melo
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Abstract

A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory index map associated to the continuous extension to A of the principal-symbol map is given. That index map takes values in K_0 of the commutator ideal E of the algebra, which is isomorphic to Z^2. It maps the K_1-class of an operator invertible modulo E to the Fredholm indices of a pair of elliptic pseudodifferentail operators on SxB, where S denotes the circle.

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Severino T. Melo. 2019-05-06. The principal-symbol index map for an algebra of pseudodifferential operators. https://arxiv.org/abs/1901.10419

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