Analytic Torsion of Z_2-graded Elliptic Complexes

Details Analytic Torsion of Z_2-graded Elliptic Complexes Analytic Torsion of Z_2-graded Elliptic Complexes

2010-01-19

arxiv.org/abs/1001.3212v2

Contemporary Mathematics, 546 (2011) 199-212

Mathematics

Differential Geometry

14 pages, typos corrected and other minor changes made in the revised version

Scientific paper

We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analytic and twisted holomorphic torsions, etc. The definition uses pseudo-differential operators and residue traces. We also study properties of analytic torsion for Z_2-graded elliptic complexes, including the behavior under variation of the metric. For compact odd dimensional manifolds, the analytic torsion is independent of the metric, whereas for even dimensional manifolds, a relative version of the analytic torsion is independent of the metric. Finally, the relation to topological field theories is studied.

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