$\eta $ invariant,Analytic torsion" /> $\eta $ invariant" /> $\eta $ invariant,Analytic torsion" />
The Mathematical Work of V. K. Patodi
Weiping Zhang
Communications in Mathematics and Statistics ›› 2014, Vol. 2 ›› Issue (3-4) : 253 -277.
The Mathematical Work of V. K. Patodi
We give a brief survey on aspects of the local index theory as developed from the mathematical works of V. K. Patodi. It is dedicated to the 70th anniversary of Patodi.
Survey / Patodi / Local index / $\eta $ invariant')">$\eta $ invariant / Analytic torsion
| [1] |
Patodi, V.K.: Collected Papers. In: Atiyah, M.F., Narasimhan, M.S. (eds.) World Scientific (1996) |
| [2] |
|
| [3] |
|
| [4] |
|
| [5] |
Patodi, V. K., (with Atiyah, M. F., Bott, R.): On the heat equations and the index theorem. Invent. Math. 19, 279–330 (1973). Errata. loc. cit. 28, 277–280 (1975) |
| [6] |
|
| [7] |
Patodi, V.K. (with Atiyah, M. F., Singer, I. M.): Spectral asymmetry and Riemannian geometry. Bull. London Math. Soc. 5, 229–234 (1973) |
| [8] |
Patodi, V.K. (with Atiyah, M. F., Singer, I. M.): Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Phil. Soc. 77, 43–69 (1975) |
| [9] |
Patodi, V.K. (with Atiyah, M. F., Singer, I. M.): Spectral asymmetry and Riemannian geometry, II. Math. Proc. Cambridge Phil. Soc. 78, 405–432 (1975) |
| [10] |
Patodi, V.K. (with Atiyah, M. F., Singer, I. M.): Spectral asymmetry and Riemannian geometry, III. Math. Proc. Cambridge Phil. Soc. 79, 71–99 (1976) |
| [11] |
Patodi, V.K.: Riemannian structures and triangulations of manifolds. In: Proceedings of the ICM1974, Vancouver (1974) |
| [12] |
|
| [13] |
Patodi, V.K. (with Dodziuk, J.): Riemannian structures and triangulations of manifolds. J. Indian Math. Soc. 40, 1–52 (1976) |
| [14] |
Patodi, V.K. (with Donnelly, H.): Spectrum and the fixed point set of isometries II. Topology 16, 1–11 (1977) |
| [15] |
|
| [16] |
|
| [17] |
|
| [18] |
|
| [19] |
Atiyah, M.F., Bott, R.: The index theorem for manifolds with boundary. In: Differential Analysis (papers presented at the Bombay Colloquium), pp. 175–186. Oxford University Press, Oxford (1964) |
| [20] |
|
| [21] |
|
| [22] |
|
| [23] |
|
| [24] |
|
| [25] |
|
| [26] |
Atiyah, M.F., Singer, I.M.: The index of elliptic operators I. Ann. Math. 87, 484–530 (1968) |
| [27] |
Atiyah, M.F., Singer, I.M.: The index of elliptic operators III. Ann. Math. 87, 546–604 (1968) |
| [28] |
|
| [29] |
|
| [30] |
Baum, P., Douglas, R. G.: $K$-homology and index theory. In: Proceedings of the Symposium on Pure and Application Mathathematics, vol. 38, pp. 117–173. American Mathematical Society, Providence (1982) |
| [31] |
Berline, N., Getzler, E., Vergne, M.: Heat Kernels and Dirac Operators. In: Grundl. Math. Wiss. Band 298, Springer-Verlag, Berlin (1992) |
| [32] |
|
| [33] |
Bismut, J.-M.: The Atiyah-Singer index theorem: a probabilitistic approach I. J. Funct. Anal. 57, 56–99 (1984) |
| [34] |
Bismut, J.-M.: The Atiyah-Singer index theorem: a probabilitistic approach II. J. Funct. Anal. 57, 329–348 (1984) |
| [35] |
|
| [36] |
Bismut, J.-M.: Index theorem and the heat equation. In: Proceedings of the ICM-1986, Berkeley (1986) |
| [37] |
Bismut, J.-M.: Local index theory and higher analytic torsion. In: Proceedings of the ICM1998 in Documenta Mathematica Extra, vol. I, pp. 143–162 (1998) |
| [38] |
|
| [39] |
Bismut, J.-M.: The hypoelliptic Dirac operator. In: Geometry and Dynamics of Groups and Spaces. Progress in Math, vol. 265, pp. 113–246. Birkhäuser, Basel (2008) |
| [40] |
|
| [41] |
Bismut, J.-M.: Hypoelliptic Laplacian and Orbital Integrals. Annals of Mathematics Studies, vol. 177. Princeton University Press, Princeton (2011) |
| [42] |
Bismut, J.-M.: Index theory and the hypoelliptic Laplacian. In: Metric and Differential Geometry. Progress in Mathemathis, vol. 297, pp. 181–232. Birkhuser/Springer, Basel (2012) |
| [43] |
Bismut, J.-M.: Hypoelliptic Laplacian and Bott–Chern cohomology. A theorem of Riemann–Roch–Grothendieck in complex geometry. Progress in Mathematics, vol. 305. Birkhuser/Springer, Cham (2013). xvi+203 pp |
| [44] |
|
| [45] |
|
| [46] |
|
| [47] |
|
| [48] |
|
| [49] |
|
| [50] |
|
| [51] |
Bismut, J.-M., Goette, S.: Families Torsion and Morse Functions. Astérisque, tom. 275. Société Mathématique, Paris (2001) |
| [52] |
Bismut, J.-M., Lebeau, G.: The Hypoelliptic Laplacian and Ray–Singer Metrics. Annals of Mathematics Studies, vol. 167. Princeton University Press, Princeton (2008) |
| [53] |
|
| [54] |
Bismut, J.-M., Zhang, W.: An Extension of a Theorem by Cheeger and Müller. Astérisque, tom. 205. Société Mathématique, Paris (1992) |
| [55] |
|
| [56] |
|
| [57] |
|
| [58] |
Brüning, J., Ma, X.: On the gluing formula for the analytic torsion. Math. Z. 273, 1085–1117 (2013). Erratum. loc. cit. 278, 615–616 (2014) |
| [59] |
|
| [60] |
|
| [61] |
Cheeger, J.: On the formulas of Atiyah–Patodi-Singer and Witten. In: Proceedings of the ICM-1986, Berkeley (1986) |
| [62] |
|
| [63] |
|
| [64] |
|
| [65] |
|
| [66] |
Dai, X., Freed, D.S.: Eta invariants and determinant lines. J. Math. Phys. 35, 5155–5194 (1994). Erratum. loc. cit. 42, 2343–2344 (2001) |
| [67] |
|
| [68] |
|
| [69] |
|
| [70] |
|
| [71] |
|
| [72] |
|
| [73] |
|
| [74] |
Duistermaat, J. J., Heckman, G.: On the variation in the chohomology of the symplectic form of the reduced phase space. Invent. Math. 69, 259–268 (1982). Addendum. 72, 153–158 (1983) |
| [75] |
|
| [76] |
|
| [77] |
|
| [78] |
|
| [79] |
|
| [80] |
|
| [81] |
|
| [82] |
|
| [83] |
Goette, S.: Torsion invariants for families. In: Dai, X., Leandre, R., Ma, X., Zhang, W. (eds.) From Probability to Geometry (II): Volume in Honor of the 60th Birthday of Jean-Michel Bismut, pp. 161–206. Astérisque, Tom. 328. Société Mathématique, Paris (2009) |
| [84] |
Goette, S.: Computations and applications of $\eta $ invariants. In: Bär, C., Lohkamp, J., Schwarz, M. (eds.) Global Differential Geometry. Springer Proceedings in Mathematics, pp. 401–433. Springer-Verlag, Berlin (2012) |
| [85] |
Hirzebruch, F.: Topological Methods in Algebraic Geometry. 3rd ed. Grundl. Math. Wiss. Band 131. Springer, Berlin (1966) |
| [86] |
|
| [87] |
|
| [88] |
|
| [89] |
|
| [90] |
|
| [91] |
Lott, J.: R/Z-index theory. Commun. Anal. Geom. 2, 279–311 (1994) |
| [92] |
Ma, X., Zhang, W.: Eta-invariant and flat vector bundles II. In: Griffiths, P. A. (ed.) Inspired by S. S. Chern. Nankai Tracts in Mathematics, Vol. 11. pp. 335–350. World Scientific, Singapore (2006) |
| [93] |
|
| [94] |
|
| [95] |
|
| [96] |
|
| [97] |
|
| [98] |
|
| [99] |
|
| [100] |
|
| [101] |
|
| [102] |
Müller, W.: The eta invariant. Séminaire Bourbaki 787, 1–25 (1993–1994) |
| [103] |
|
| [104] |
|
| [105] |
|
| [106] |
|
| [107] |
|
| [108] |
|
| [109] |
Singer, I. M.: The $\eta $-invariant and the index. In: Mathematical Aspects of String Theory, Advanced Series in Mathematical Physics, vol. 1, pp. 239–258. World Scientific Publishing, Singapore (1987) |
| [110] |
|
| [111] |
|
| [112] |
|
| [113] |
|
| [114] |
|
| [115] |
|
| [116] |
|
/
| 〈 |
|
〉 |