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THE INDEX OF TOEPLITZ OPERATORS ON FREE TRANSFORMATION GROUP C*-ALGEBRAS

Published online by Cambridge University Press:  18 January 2002

EFTON PARK
Affiliation:
Department of Mathematics, Texas Christian University, Fort Worth, Texas 76129, USA; e.park@tcu.edu
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Abstract

Let Γ be a discrete group acting on a compact manifold X, let V be a Γ-equivalent Hermitian vector bundle over X, and let D be a first-order elliptic self-adjoint Γ-equivalent differential operator acting on sections of V. This data is used to define Toeplitz operators with symbols in the transformation group C*-algebra C(X)[rtimes ]Γ, and it is shown that if the symbol of such a Toeplitz operator is invertible, then the operator is Fredholm. In the case where Γ is finite and acts freely on X, a geometric-topological formula for the index is stated that involves an explicitly constructed differential form associated to the symbol.

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2002

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