A survey of the hypoelliptic Laplacian
Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 39-69. 
@incollection{AST_2008__322__39_0,
     author = {Bismut, Jean-Michel},
     title = {A survey of the hypoelliptic {Laplacian}},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (II) - Volume en l'honneur de Jean-Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     pages = {39--69},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {322},
     year = {2008},
     mrnumber = {2521653},
     zbl = {1180.58001},
     language = {en},
     url = {http://www.numdam.org/item/AST_2008__322__39_0/}
}
TY  - CHAP
AU  - Bismut, Jean-Michel
TI  - A survey of the hypoelliptic Laplacian
BT  - Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon
AU  - Collectif
ED  - Hijazi Oussama
T3  - Astérisque
PY  - 2008
SP  - 39
EP  - 69
IS  - 322
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2008__322__39_0/
LA  - en
ID  - AST_2008__322__39_0
ER  - 
%0 Book Section
%A Bismut, Jean-Michel
%T A survey of the hypoelliptic Laplacian
%B Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon
%A Collectif
%E Hijazi Oussama
%S Astérisque
%D 2008
%P 39-69
%N 322
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2008__322__39_0/
%G en
%F AST_2008__322__39_0
Bismut, Jean-Michel. A survey of the hypoelliptic Laplacian, dans Géométrie différentielle, physique mathématique, mathématiques et société (II) - Volume en l'honneur de Jean-Pierre Bourguignon, Astérisque, no. 322 (2008), pp. 39-69. http://www.numdam.org/item/AST_2008__322__39_0/

[1] A. Berthomieu & J.-M. Bismut - "Quillen metrics and higher analytic torsion forms", J. reine angew. Math. 457 (1994), p. 85-184. | EuDML | MR | Zbl

[2] J.-M. Bismut - "Koszul complexes, harmonic oscillators, and the Todd class", J. Amer. Math. Soc. 3 (1990), p. 159-256. | DOI | MR | Zbl

[3] J.-M. Bismut, "The hypoelliptic Laplacian on the cotangent bundle", J. Amer. Math. Soc. 18 (2005), p. 379-476. | DOI | MR | Zbl

[4] J.-M. Bismut, "The hypoelliptic Laplacian and Chern-Gauss-Bonnet", in Differential geometry and physics, Nankai Tracts Math., vol. 10, World Sci. Publ., Hackensack, NJ, 2006, p. 38-52. | DOI | MR | Zbl

[5] J.-M. Bismut, "The hypoelliptic Dirac operator", in Geometry and dynamics of groups and spaces, Progr. Math., vol. 265, Birkhäuser, 2008, p. 113-246. | DOI | MR | Zbl

[6] J.-M. Bismut, "Loop spaces and the hypoelliptic Laplacian", Comm. Pure Appl. Math. 61 (2008), p. 559-593. | DOI | MR | Zbl

[7] J.-M. Bismut & G. Lebeau - "Complex immersions and Quillen metrics", Publ. Math. I.H.É.S. 74 (1991). | EuDML | Numdam | MR | Zbl

[8] J.-M. Bismut & G. Lebeau, The hypoelliptic Laplacian and Ray-Singer metrics, Annals of Mathematics Studies, vol. AM-167, Princeton University Press, 2008. | MR | Zbl

[9] J.-M. Bismut & W. P. Zhang - "An extension of a theorem by Cheeger and Müller", Astérisque 205 (1992), p. 235. | Numdam | MR | Zbl

[10] J.-M. Bismut & W. P. Zhang, "Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle", Geom. Funct. Anal. 4 (1994), p. 136-212. | DOI | EuDML | MR | Zbl

[11] J. Cheeger - "Analytic torsion and the heat equation", Ann. of Math. 109 (1979), p. 259-322. | DOI | MR | Zbl

[12] B. Helffer & J. Sjöstrand - "Puits multiples en mécanique semi-classique. IV. Étude du complexe de Witten", Comm. Partial Differential Equations 10 (1985), p. 245-340. | DOI | MR | Zbl

[13] N. Hitchin - "Harmonic spinors", Advances in Math. 14 (1974), p. 1-55. | MR | Zbl

[14] L. Hörmander - "Hypoelliptic second order differential equations", Acta Math. 119 (1967), p. 147-171. | DOI | MR | Zbl

[15] A. Kolmogoroff - "Zufällige Bewegungen (zur Theorie der Brownschen Bewegung)", Ann. of Math. 35 (1934), p. 116-117. | DOI | MR | Zbl

[16] W. Müller - "Analytic torsion and R-torsion of Riemannian manifolds", Adv. in Math. 28 (1978), p. 233-305. | MR | Zbl

[17] D. Quillen - "Determinants of Cauchy-Riemann operators on Riemann surfaces", Functional Anal. Appl. 19 (1985), p. 31-34. | DOI | MR | Zbl

[18] D. Quillen, "Superconnections and the Chern character", Topology 24 (1985), p. 89-95. | DOI | MR | Zbl

[19] D. B. Ray & I. M. Singer - "R-torsion and the Laplacian on Riemannian manifolds", Advances in Math. 7 (1971), p. 145-210. | MR | Zbl

[20] E. Witten - "Supersymmetry and Morse theory", J. Differential Geom. 17 (1982), p. 661-692. | DOI | MR | Zbl