S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations : bounds on eigenfunctions of N -body Schrödinger operators, Mathematical Notes, vol.29, 1982.
DOI : 10.1515/9781400853076

P. Alsholm and G. Schmidt, Spectral and scattering theory for Schrödinger operators. Various Publications Series, Matematisk Institut, issue.7, 1969.
DOI : 10.1007/bf00252679

F. A. Berezin and M. A. Shubin, The Schrödinger Equation. Mathematics and its Applications, 1991.

R. Bott, Lectures on Morse theory, old and new, Bulletin of the American Mathematical Society, vol.7, issue.2, pp.331-358, 1982.
DOI : 10.1090/S0273-0979-1982-15038-8

R. Bott and L. W. Tu, Differential Forms in Algebraic Topology (Graduate Texts in Mathematics), 1995.

D. Burghelea, Lectures on witten helffer sjörstrand theory, 1998.

B. Candelpergher and J. Nosmas, Properties spectrales d'operateurs differentials asymptotiques autoadjoints, Communications in Partial Differential Equations, vol.16, issue.2, pp.137-167, 1984.
DOI : 10.1080/03605308408820328

D. Castelvecchi, The foliated morse inequalities. Thesis, 2001.

P. Chand and J. Hoekstra, A review of the semi classical wkb approximation and its usefulness in the study of quantum systems, 2001.

K. Chang, Infinite-dimensional Morse theory and multiple solution problems, Progress in Nonlinear Differential Equations and their Applications, 1993.
DOI : 10.1007/978-1-4612-0385-8

C. Cohen-tannoudji, B. Diu, and F. Laloë, Mécanique quantique I. Hermann, 1997.

A. Connes, Sur la theorie non commutative de l???integration, Lecture Notes in Math, vol.725, pp.19-143, 1978.
DOI : 10.1007/BFb0062614

A. Connes, A survey of foliations and operator algebras, Proceedings of Symposia in Pure Maths, pp.521-628, 1982.
DOI : 10.1090/pspum/038.1/679730

A. Connes, Noncommutative geometry, 1994.

A. Connes and T. Fack, Morse inequalities for measured foliations, 1991.

A. Connes and T. Fack, c * -algebras and elliptic theory, Trends in Mathematics, pp.61-72, 2006.

R. Coqueraux, Espaces fibrés et connexions, Livre sur internet, 2002.

O. Cornea and A. Ranicki, Rigidity and gluing for Morse and Novikov complexes, Journal of the European Mathematical Society, vol.5, issue.4, pp.343-394, 2003.
DOI : 10.1007/s10097-003-0052-6

H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger operators with application to quantum mechanics and global geometry. Texts and Monographs in Physics, 1987.

G. and D. Rham, Variétés différentiables. Formes, courants, formes harmoniques. Hermann , Paris, 1973. Troisième édition revue et augmentée, Publications de l, 1222.

J. Demailly, Analyse numérique et équations différentielles, 1996.

M. Demazure, Catastrophes et bifurcations. Editions Marketing, 1989.

J. Dodziuk, De Rham-Hodge theory for L2-cohomology of infinite coverings, Topology, vol.16, issue.2, pp.157-165, 1977.
DOI : 10.1016/0040-9383(77)90013-1

J. Dodziuk, Sobolev spaces of differential forms and de Rham-Hodge isomorphism, Journal of Differential Geometry, vol.16, issue.1, pp.63-73, 1981.
DOI : 10.4310/jdg/1214435988

V. K. Dodziuk and J. Patodi, RIEMANNIAN STRUCTURES AND TRIANGULATIONS OF MANIFOLDS, J. Indian Math. Soc, vol.40, pp.1-52, 1976.
DOI : 10.1142/9789812830210_0013

B. Doubrovine, S. Novikov, and A. Fomenko, Géométrie contemporaine. Méthodes et applications, tomes I, II & III, 1982.

J. L. Dupont, Simplicial de rham cohomology and characteristic classes of flat bundles, Topology, vol.15, issue.3, pp.233-245, 1976.
DOI : 10.1016/0040-9383(76)90038-0

Y. M. Eliashberg and N. M. Mishachev, Wrinkling on smooth mappings ii. wrinkling of embeddings and k. igusa' theorem. Topology, pp.711-732, 2000.

T. Fack, Sur la notion de valeur caractéristique, J. Operator Theory, vol.7, issue.2, pp.307-333, 1982.

T. Fack and H. Kosaki, -measurable operators, Pacific Journal of Mathematics, vol.123, issue.2, pp.269-300, 1986.
DOI : 10.2140/pjm.1986.123.269

URL : https://hal.archives-ouvertes.fr/hal-00813575

K. O. Friedricks, Perturbation of Spectra in Hilbert Space (Lectures in Applied Math V003), 1967.

S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry. Universitext, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00002870

A. Gramain, Topologie des surfaces. Presses Universitaires de France, Collection SUP : " Le Mathématicien, 1971.

G. Hector and U. Hirsch, Introduction to the geometry of foliations, Foliations on compact surfaces, fundamentals for arbitrary codimension, and holonomy, 1986.

G. Hector and U. Hirsch, Introduction to the geometry of foliations, Part B. Aspects of Mathematics E3. Friedr. Vieweg & Sohn, 1987.

J. L. Heitsch and C. Lazarov, Homotopy invariance of foliation Betti numbers, Inventiones mathematicae, vol.49, issue.1, pp.321-347, 1991.
DOI : 10.1007/BF01245079

B. Helffer, Etude du laplacien de witten associé à une fonction de morse dégénérée, 1985.

B. Helffer, Semiclassical analysis, Witten Laplacians, and statistical mechanics, volume 1 of Series on Partial Differential Equations and Applications, 2002.

B. Helffer, 30 ans d'analyse semi-classique : Bibliographie commentée, 2003.

B. Helffer, Introduction to the semi-classical method for the schrödinger operator with magnetic field, 2004.

B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit I, Communications in Partial Differential Equations, vol.52, issue.2, pp.337-408, 1984.
DOI : 10.1080/03605308408820335

B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit iii

B. Helffer and J. Sjöstrand, Puits multiples en limite semi-classique ii -interaction moléculaire-symétries-perturbations. Annales de l'IHP (section Physique théorique, pp.127-212, 1985.

B. Helffer and J. Sjöstrand, Puits multiples en mecanique semi-classique iv etude du complexe de witten, Communications in Partial Differential Equations, vol.17, issue.4, pp.245-340, 1985.
DOI : 10.1080/03605308508820379

B. Helffer and J. Sjöstrand, Effet tunnel pour l'équation de schrödinger avec champ magnétique, 1987.

G. Henniart, Les inégalités de Morse (d'après E. Witten), 1985, Seminar Bourbaki, vol.84, 1983.

M. Hilsum, Signature operator on lipschitz manifolds and unbounded Kasparov bimodules, Lecture Notes Math, vol.163, issue.2, pp.254-288, 1985.
DOI : 10.1007/BF01425417

K. Igusa, The space of framed functions, Transactions of the American Mathematical Society, vol.301, issue.2, pp.437-477, 1987.
DOI : 10.1090/S0002-9947-1987-0882699-7

K. Igusa, The stability theorem for smooth pseudoisotopies, K-Theory, vol.2, issue.1-2, pp.1-355, 1988.
DOI : 10.1007/BF00533643

K. Igusa, C1 Local parametrized morse theory, Topology and its Applications, vol.36, issue.3, pp.209-231, 1990.
DOI : 10.1016/0166-8641(90)90046-5

URL : http://doi.org/10.1016/0166-8641(90)90046-5

T. Kato, Perturbation Theory for Linear Operators, 1995.

Y. A. Kordyukov, Noncommutative spectral geometry of riemannian foliations, Manuscripta Mathematica, vol.2, issue.4, pp.45-73, 1997.
DOI : 10.1007/BF02677838

J. Lafontaine, Introduction aux varietes differentielles, 1996.

A. Messiah, Mécanique quantique tome 1. Dunod, 2003.

J. Milnor, Morse theory. Based on lecture notes by M. Spivak and R. Wells, Annals of Mathematics Studies, issue.51, 1963.

G. Mircea, A local solution of the schrödinger equation, Journal of Physics A : Mathematical and General, issue.43, pp.318669-8676, 1998.

A. Mohamed and J. Nourrigat, Borne inférieure du spectre de l'opérateur de Schrödinger . (Lower bound for the spectrum of the Schrödinger operator), 1988.

C. C. Moore, C. Schochet, and R. J. Zimmer, Global analysis on foliated spaces, volume 9 of Mathematical Sciences Research Institute Publications, With appendices by S. Hurder, 1988.

P. K. Patnaik, Rayleigh-Schr??dinger perturbation theory for the anharmonic oscillator, Physical Review D, vol.35, issue.4, pp.1234-1238, 1987.
DOI : 10.1103/PhysRevD.35.1234

M. M. Peixoto, On Structural Stability, The Annals of Mathematics, vol.69, issue.1, pp.199-222, 1959.
DOI : 10.2307/1970100

M. Q. Phan, Introduction à la géométrie des variétés différentielles. Dunod, 1969.

M. Pozniak, Floer homology, Novikov rings and clean intersections, Amer. Math. Soc. Transl, vol.196, issue.2, pp.119-181, 1999.
DOI : 10.1090/trans2/196/08

B. L. Reinhart, Differential geometry of foliations The fundamental integrability problem, Mathematics and Related Areas, 1983.

L. Schwartz, Théorie des distributions Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, 1966.

M. Schwarz, Morse Homology (Progress in Mathematics) Birkhäuser Basel, 2004.

B. Simon, Instantons, double wells and large deviations, Bulletin of the American Mathematical Society, vol.8, issue.2, pp.323-326, 1983.
DOI : 10.1090/S0273-0979-1983-15104-2

B. Simon, Semiclassical analysis of low lying eigenvalues. I. non-degenerate minima : asymptotic expansions, Ann. Inst. Henri Poincaré (A), vol.38, issue.3, pp.295-308, 1983.

B. Simon, Semiclassical Analysis of Low Lying Eigenvalues, II. Tunneling, The Annals of Mathematics, vol.120, issue.1, pp.89-118, 1984.
DOI : 10.2307/2007072

F. Truc, Valeurs propres semi-classiques d'un opérateur de schrödinger avec potentiel dégénéré, 1998.

J. Weber, The Morse???Witten complex via dynamical systems, Expositiones Mathematicae, vol.24, issue.2, 2004.
DOI : 10.1016/j.exmath.2005.09.001

E. Witten, Supersymmetry and Morse theory, Journal of Differential Geometry, vol.17, issue.4, pp.661-692, 1982.
DOI : 10.4310/jdg/1214437492