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Holomorphic equivariant analytic torsions. (English) Zbl 0974.58033
The authors construct and compare two natural definitions of equivariant holomorphic torsion. They show the comparison formula is compatible with the embedding formulas for the analytic torsion forms and for the equivariant analytic torsion.
§0 is a brief introduction to the subject, §1 introduces the equivariant holomorphic analytic torsion, §2 discusses the equivariant infinitesimal analytic torsion forms, §3 deals with the equivariant Bott-Chern currents, and §4 describes the harmonic oscillator and the genus I. §5 presents a comparison formula for the equivariant torsions, §6 gives a proof of the comparison formula, and §7 constructs the families of equivariant analytic torsion forms. The final two sections prove results used in §6.

MSC:
58J52 Determinants and determinant bundles, analytic torsion
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