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Refined analytic torsion on manifolds with boundary

Boris Vertman

Geometry & Topology 13 (2009) 1989–2027
Bibliography
1 S Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962) 119 MR0147774
2 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797
3 N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, Grund. der Math. Wissenschaften 298, Springer (1992) MR1215720
4 B Booß-Bavnbek, M Lesch, C Zhu, The Calderon projection: new definition and applications arXiv:0803.4160
5 M Braverman, T Kappeler, Comparison of the refined analytic and the Burghelea–Haller torsions, Ann. Inst. Fourier (Grenoble) 57 (2007) 2361 MR2394545
6 M Braverman, T Kappeler, Refined analytic torsion as an element of the determinant line, Geom. Topol. 11 (2007) 139 MR2302591
7 M Braverman, T Kappeler, A canonical quadratic form on the determinant line of a flat vector bundle, Int. Math. Res. Not. (2008) MR2428856
8 M Braverman, T Kappeler, Refined analytic torsion, J. Differential Geom. 78 (2008) 193 MR2394022
9 J Brüning, M Lesch, Hilbert complexes, J. Funct. Anal. 108 (1992) 88 MR1174159
10 J Brüning, M Lesch, Kähler–Hodge theory for conformal complex cones, Geom. Funct. Anal. 3 (1993) 439 MR1233862
11 D Burghelea, L Friedlander, T Kappeler, Meyer–Vietoris type formula for determinants of elliptic differential operators, J. Funct. Anal. 107 (1992) 34 MR1165865
12 D Burghelea, S Haller, Complex-valued Ray–Singer torsion, J. Funct. Anal. 248 (2007) 27 MR2329682
13 D Burghelea, S Haller, Complex-valued Ray–Singer torsion II arXiv:math/0610875
14 J Cheeger, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983) MR730920
15 M Farber, Combinatorial invariants computing the Ray–Singer analytic torsion, Differential Geom. Appl. 6 (1996) 351 MR1422341
16 M Farber, V Turaev, Poincaré–Reidemeister metric, Euler structures, and torsion, J. Reine Angew. Math. 520 (2000) 195 MR1748274
17 P B Gilkey, Invariance theory, the heat equation, and the Atiyah–Singer index theorem, Studies in Advanced Math., CRC Press (1995) MR1396308
18 P B Gilkey, L Smith, The eta invariant for a class of elliptic boundary value problems, Comm. Pure Appl. Math. 36 (1983) 85 MR680084
19 P B Gilkey, L Smith, The twisted index problem for manifolds with boundary, J. Differential Geom. 18 (1983) 393 MR723812
20 R T Huang, Refined analytic torsion: comparison theorems and examples, Illinois J. Math. 51 (2007) 1309 MR2417429
21 T Kato, Perturbation theory for linear operators, Grund. der Math. Wissenschaften 132, Springer (1976) MR0407617
22 F F Knudsen, D Mumford, The projectivity of the moduli space of stable curves. I. Preliminaries on “det” and “Div”, Math. Scand. 39 (1976) 19 MR0437541
23 W Lück, Analytic and topological torsion for manifolds with boundary and symmetry, J. Differential Geom. 37 (1993) 263 MR1205447
24 W Müller, Analytic torsion and $R$–torsion for unimodular representations, J. Amer. Math. Soc. 6 (1993) 721 MR1189689
25 L Paquet, Problèmes mixtes pour le système de Maxwell, Ann. Fac. Sci. Toulouse Math. $(5)$ 4 (1982) 103 MR687546
26 D B Ray, I M Singer, $R$–torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971) 145 MR0295381
27 R Seeley, Analytic extension of the trace associated with elliptic boundary problems, Amer. J. Math. 91 (1969) 963 MR0265968
28 R Seeley, The resolvent of an elliptic boundary problem, Amer. J. Math. 91 (1969) 889 MR0265764
29 G Su, W Zhang, A Cheeger–Müller theorem for symmetric bilinear torsions, Chin. Ann. Math. Ser. B 29 (2008) 385 MR2429629
30 V Turaev, Euler structures, nonsingular vector fields, and Reidemeister-type torsions, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 607, 672 MR1013714
31 V Turaev, Torsion invariants of $\mathrm{Spin}^c$–structures on $3$–manifolds, Math. Res. Lett. 4 (1997) 679 MR1484699
32 B Vertman, Gluing formula for refined analytic torsion arXiv:0808.0451
33 S M Vishik, Generalized Ray–Singer conjecture. I. A manifold with a smooth boundary, Comm. Math. Phys. 167 (1995) 1 MR1316501