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A uniform upper bound for Fredholm index of quasi Laplace operators on a compact parallelizable manifold
Assume that $M$ is a compact parallelizable manifold. Is there an upper bound for the absolute value of Fredholm index of all operators in the form $D=\sum_{i=1}^n \partial^2/\partial{X_i^2}$ where $\{X_1,X_2,\ldots,X_n\}$ is a global smooth frame?
