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The Index of Toeplitz Operators on Free Transformation Group C*-Algebras
Authors:Park  Efton
Institution:Department of Mathematics, Texas Christian University Fort Worth, Texas 76129, USA; e.park{at}tcu.edu
Abstract:Let {Gamma} be a discrete group acting on a compact manifold X, letV be a {Gamma}-equivalent Hermitian vector bundle over X, and let Dbe a first-order elliptic self-adjoint {Gamma}-equivalent differentialoperator acting on sections of V. This data is used to defineToeplitz operators with symbols in the transformation groupC*-algebra C(X){rtimes}{Gamma}, and it is shown that if the symbol of sucha Toeplitz operator is invertible, then the operator is Fredholm.In the case where {Gamma} is finite and acts freely on X, a geometric-topologicalformula for the index is stated that involves an explicitlyconstructed differential form associated to the symbol. 2000Mathematics Subject Classification 47A53 (primary), 19K56, 47B35,46L87 (secondary).
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