[A deformation of Hodge theory on the cotangent bundle]
In this Note, we announce the construction of a natural deformation of Hodge theory. In particular we obtain the adjoint of the de Rham operator on the cotangent bundle with respect to a hermitian form of nontrivial signature.
Dans cette Note, on annonce une construction d'une déformation de la théorie de Hodge. On construit en particulier l'adjoint de l'opérateur de de Rham sur le fibré cotangent relativement à une forme hermitienne de signature non triviale.
Accepted:
Published online:
Jean-Michel Bismut 1
@article{CRMATH_2004__338_6_471_0, author = {Jean-Michel Bismut}, title = {Une d\'eformation de la th\'eorie de {Hodge} sur le fibr\'e cotangent}, journal = {Comptes Rendus. Math\'ematique}, pages = {471--476}, publisher = {Elsevier}, volume = {338}, number = {6}, year = {2004}, doi = {10.1016/j.crma.2004.01.012}, language = {fr}, }
Jean-Michel Bismut. Une déformation de la théorie de Hodge sur le fibré cotangent. Comptes Rendus. Mathématique, Volume 338 (2004) no. 6, pp. 471-476. doi : 10.1016/j.crma.2004.01.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.01.012/
[1] J.-M. Bismut, The hypoelliptic Laplacian on the cotangent bundle (2004) à paraître
[2] J.-M. Bismut, Le laplacien hypoelliptique sur le fibré cotangent. C. R. Math. Acad. Sci. Paris 338 (2004) sous presse
[3] J.-M. Bismut, Une déformation en famille du complexe de de Rham-Hodge, C. R. Math. Acad. Sci. Paris 338 (2004) sous presse
[4] J.-M. Bismut, G. Lebeau, The analysis of the hypoelliptic Laplacian (2004) à paraître
[5] An extension of a theorem by Cheeger and Müller, Astérisque (1992) no. 205, p. 235 (With an appendix by François Laudenbach)
[6] Milnor and Ray–Singer metrics on the equivariant determinant of a flat vector bundle, Geom. Funct. Anal., Volume 4 (1994) no. 2, pp. 136-212
[7] Analytic torsion and the heat equation, Ann. of Math. (2), Volume 109 (1979) no. 2, pp. 259-322
[8] Puits multiples en mécanique semi-classique. IV. Étude du complexe de Witten, Comm. Partial Differential Equations, Volume 10 (1985) no. 3, pp. 245-340
[9] Hypoelliptic second order differential equations, Acta Math., Volume 119 (1967), pp. 147-171
[10] The projectivity of the moduli space of stable curves. I. Preliminaries on “det” and “Div”, Math. Scand., Volume 39 (1976) no. 1, pp. 19-55
[11] Zufällige Bewegungen (zur Theorie der Brownschen Bewegung), Ann. of Math. (2), Volume 35 (1934) no. 1, pp. 116-117
[12] Superconnections, Thom classes, and equivariant differential forms, Topology, Volume 25 (1986) no. 1, pp. 85-110
[13] Analytic torsion and R-torsion of Riemannian manifolds, Adv. in Math., Volume 28 (1978) no. 3, pp. 233-305
[14] Determinants of Cauchy–Riemann operators on Riemann surfaces, Funct. Anal. Appl., Volume 19 (1985) no. 1, pp. 31-34
[15] Supersymmetry and Morse theory, J. Differential Geom., Volume 17 (1983) no. 4, pp. 661-692
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