We derive the formulas expressing the topological characteristics (Betti numbers) of 3d-manifold with boundary through its Dirichlet-to-Neumann maps associated with scalar and vector harmonic fields.
@article{1618,
title = {Some remarks on the impedance tomography problem for 3d-manifolds},
journal = {CUBO, A Mathematical Journal},
volume = {7},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/1618}
}
Belishev, M.I. Some remarks on the impedance tomography problem for 3d-manifolds. CUBO, A Mathematical Journal, Tome 7 (2005) . http://gdmltest.u-ga.fr/item/1618/