Sur le specter des fibers en tore qui s'effondrent

摘要

We consider torus bundles over S~1 and T~2 with solmanifold structure, and analyze the behavior of the Laplacian acting on left-invariant differential forms under homogeneous collapsings with bounded diameter and bounded sectional curvature. Whe show how the number of small eigenvalues depends on the topology of the bundle and the geometry of the collapsing.