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ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS

  • Jean-Michel Bismut (a1), Xiaonan Ma (a2) and Weiping Zhang (a3)
Abstract

We use Toeplitz operators to evaluate the leading term in the asymptotics of the analytic torsion forms associated with a family of flat vector bundles $F_{p}$ . For $p\in \mathbf{N}$ , the flat vector bundle $F_{p}$ is the direct image of $L^{p}$ , where $L$ is a holomorphic positive line bundle on the fibres of a flat fibration by compact Kähler manifolds. The leading term of the analytic torsion forms is the integral along the fibre of a locally defined differential form.

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References
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