Heat kernels on covering spaces and topological invariants (Q1203620)

The author considers the concept of analytic torsion for covering spaces. This torsion is defined when the heat kernels on \(p\)-forms decay like a power \(-\alpha_ p\) of \(t\), as \(t \to \infty\). The exponent \(\alpha_ p\) is the Novikov-Shubin invariant. Examples are given where \(\alpha_ p\) is arbitrarily close to 0. Various estimates and calculations are given for Heisenberg groups and locally symmetric spaces. Also, \(\alpha_ p\) is proved to be a topological invariant.