New Proof of the Cheeger-Müller Theorem

Annals of Global Analysis and Geometry

Volumn 23, Issue 1, 2003, Pages 77-92

  Braverman, Maxim ^a  

^a NORTHEASTERN UNIVERSITY   (United States)

Author keywords

Analytic torsion; Ray Singer

Indexed keywords

EID: 0037212567     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021227705930     Document Type: Article

References (22)

1. Bismut, J.-M., Gillet, H. and Soulé, C.: Analytic torsion and holomorphic determinant bundles, i, Commun. Math. Phys. 115 (1988), 49-78.
2. Bismut, J.-M. and Zhang, W.: An extension of a theorem by Cheeger and Müller, Astérisque 205 (1992).
3. Bismut, J.-M. and Zhang, W.: Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle, Geom. Funct. Anal. 4 (1994), 136-212.
4. Burghelea, D., Friedlander, L. and Kappeler, T.: Mayer-Vietoris type formula for determinants of elliptic differential operators, J. Funct. Anal. 107 (1992), 34-65.
5. Burghelea, D., Friedlander, L. and Kappeler, T.: Asymptotic expansion of the Witten deformation of the analytic torsion, J. Funct. Anal. 137 (1996), 320-363.
6. Burghelea, D., Friedlander, L., Kappeler, T. and McDonald, P.: Analytic and Reidemeister torsion for representations in finite type Hilbert modules, Geom. Funct. Anal. 6 (1996), 751-859.
7. Cheeger, J.: Analytic torsion and the heat equation, Ann. of Math. 109 (1979), 259-300.
8. Cycon, H. L., Froese, R. G., Kirsch, W. and Simon, B.: Schrödinger Operators with Applications to Quantum Mechanics and Global Geometry, Texts Monographs Phys., Springer-Verlag, Berlin, 1987.
9. Helffer, B. and Sjöstrand, J.: Puits multiples en limite semi-classicue. IV. étude du complexe de Witten, Comm. Partial Differential Equations 10 (1985), 245-340.
10. Knudsen, F. F. and Mumford, D.: The projectivity of the moduli spaces of stable curves, I: Preliminaries on 'det' and 'div', Math. Scand. 39 (1976), 19-55.
11. Milnor, J.: Lectures on the h-Cobordism Theorem, Princeton Univ. Press, Princeton, NJ, 1965.
12. Milnor, J.: Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426.
13. Müller, W.: Analytic torsion and R-torsion on Riemannian manifolds, Adv. Math. 28 (1978), 233-305.
14. Müller, W.: Analytic torsion and R-torsion for unimodular representation, J. Amer. Math. Soc. 6 (1993), 721-753.
15. Ray, D. B. and Singer, I. M.: R-torsion and the Laplacian on Riemannian manifolds, Adv. Math. 7 (1971), 145-210.
16. Seeley, R.: Complex powers of elliptic operators, Proc. Sympos. Pure Appl. Math. Amer. Math. Soc. 10 (1967), 288-307.
17. Shubin, M. A.: Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, 1980.
18. Shubin, M. A.: Semiclassical asymptotics on covering manifolds and Morse inequalities, Geom. Funct. Anal. 6 (1996), 370-409.
19. Smale, S.: On gradient dynamical systems, Ann. of Math. 74 (1961), 199-206.
20. Smale, S.: Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817.
21. Thom, R.: Sur une partition en cellules associée à une fonction sur une variété, C.R. Acad. Sci. Paris, Sér. A 228 (1949), 661-692.
22. Witten, E.: Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), 661-692.