Sur le spectre du laplacien des fibrés en tores qui s'effondrent

Abstract

We study the small eigenvalues of the Hodge Laplacian on collaping torus bundles with bounded curvature. In the first part of this dissertation, we consider examples of bundles on S^1 and T^2 with homogeneous structure. In the second part, we give a lower bound of the first non-zero eigenvalue of the 1-form Laplacian on principal torus bundles.

PhD thesis, 77 pages, in french. v3: cleanup and typographic corrections