Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form

Abstract For a complex flat vector bundle over a fibered manifold, we consider the 1-parameter family of certain deformed sub-signature operators introduced by Ma-Zhang in [Math. Ann. 340: 569–624, 340]. We compute the adiabatic limit of the Bismut-Freed connection associated to this family and show that the Bismut-Lott analytic torsion form shows up naturally under this procedure.

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