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

Summary: Adiabatic limit, Bismut-Freed connection, and
the real analytic torsion form
Xianzhe Dai
and Weiping Zhang
Dedicated to Richard B. Melrose for his sixtieth birthday
Abstract
For a complex flat vector bundle over a fibered manifold, we con-
sider the 1-parameter family of certain deformed sub-signature operators
introduced by Ma-Zhang in [MZ]. 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 proce-
dure.
1 Introduction
Adiabatic limit refers to the geometric degeneration when metric in certain
directions are blown up, while the remaining directions are kept fixed.
Typically, the underlying manifold has a so called fibration structure (or
fiber bundle structure). That is
Z - M

- B,

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics