Abstract :
In the spirit of Ray and Singer we define a complex-valued analytic torsion using non-selfadjoint Laplacians.
We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally
this analytically defined invariant computes the complex-valued Reidemeister torsion, including its phase.
We establish this conjecture in some non-trivial situations.
© 2007 Elsevier Inc. All rights reserved
Keywords :
Müller theorem , Co-Euler structures , Dirac operator , Euler structures , Heat kernel , Ray–Singer torsion , Reidemeister torsion , analytic torsion , combinatorial torsion , Anomaly formula , Bismut–Zhang , Cheeger , asymptotic expansion
