We give an explicit formula for the L2 analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic torsion of the cone is the finite part of the limit obtained collapsing one of the boundaries, of the ratio of the analytic torsion of the frustum to a regularising factor. We show that the regularising factor comes from the set of the non square integrable eigenfunctions of the Laplace Beltrami operator on the cone.
Hartmann, L., Spreafico, M. (2017). The analytic torsion of the finite metric cone over a compact manifold. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 69(1), 311-371 [10.2969/jmsj/06910311].
The analytic torsion of the finite metric cone over a compact manifold
Spreafico M.
2017
Abstract
We give an explicit formula for the L2 analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic torsion of the cone is the finite part of the limit obtained collapsing one of the boundaries, of the ratio of the analytic torsion of the frustum to a regularising factor. We show that the regularising factor comes from the set of the non square integrable eigenfunctions of the Laplace Beltrami operator on the cone.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.