A generalization of analytic torsion via differential forms on spaces of metrics
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Publication:6319744
arXiv1905.13721MaRDI QIDQ6319744
Publication date: 31 May 2019
Abstract: We introduce multi-torsion, a spectral invariant generalizing Ray-Singer analytic torsion. We define multi-torsion for compact manifolds with a certain local geometric product structure that gives a bigrading on differential forms. We prove that multi-torsion is metric-independent in a suitable sense. Our definition of multi-torsion is inspired by an interpretation of each of analytic torsion and the eta invariant as a regularized integral of a closed differential form on a space of metrics on a vector bundle or on a space of elliptic operators. We generalize the Stokes' theorem argument explaining the dependence of torsion and eta on the geometric data used to define them to the local product setting to prove our metric-independence theorem for multi-torsion.
Differential complexes (58J10) Eta-invariants, Chern-Simons invariants (58J28) Determinants and determinant bundles, analytic torsion (58J52) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
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