#### Volume 14, issue 1 (2014)

 1 L Alvarez-Gaumé, E Witten, Gravitational anomalies, Nuclear Phys. B 234 (1984) 269 MR736803 2 O Alvarez, I M Singer, B Zumino, Gravitational anomalies and the family's index theorem, Comm. Math. Phys. 96 (1984) 409 MR769356 3 M F Atiyah, $K$–theory, W A Benjamin (1967) MR0224083 4 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797 5 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, II, Math. Proc. Cambridge Philos. Soc. 78 (1975) 405 MR0397798 6 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, III, Math. Proc. Cambridge Philos. Soc. 79 (1976) 71 MR0397799 7 M F Atiyah, I M Singer, Dirac operators coupled to vector potentials, Proc. Nat. Acad. Sci. U.S.A. 81 (1984) 2597 MR742394 8 N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, Grundl. Math. Wissen. 298, Springer (1992) MR1215720 9 J M Bismut, The Atiyah–Singer index theorem for families of Dirac operators: Two heat equation proofs, Invent. Math. 83 (1985) 91 MR813584 10 J M Bismut, D S Freed, The analysis of elliptic families, I: Metrics and connections on determinant bundles, Comm. Math. Phys. 106 (1986) 159 MR853982 11 J M Bismut, D S Freed, The analysis of elliptic families, II: Dirac operators, eta invariants, and the holonomy theorem, Comm. Math. Phys. 107 (1986) 103 MR861886 12 K Chandrasekharan, Elliptic functions, Grundl. Math. Wissen. 281, Springer (1985) MR808396 13 D E Diaconescu, G Moore, E Witten, $E_8$ gauge theory, and a derivation of $K$–theory from M–theory, Adv. Theor. Math. Phys. 6 (2002) 1031 MR1982693 14 L D Faddeev, Operator anomaly for the Gauss law, Phys. Lett. B 145 (1984) 81 MR757331 15 D S Freed, $\mathbf{Z}/k$–manifolds and families of Dirac operators, Invent. Math. 92 (1988) 243 MR936082 16 F Hirzebruch, Topological methods in algebraic geometry, Grundl. Math. Wissen. 131, Springer (1966) MR0202713 17 F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, Aspects of Mathematics 20, Friedr. Vieweg & Sohn (1992) MR1189136 18 P S Landweber, Elliptic cohomology and modular forms, from: "Elliptic curves and modular forms in algebraic topology" (editor P S Landweber), Lecture Notes in Math. 1326, Springer (1988) 55 MR970281 19 K Liu, Modular invariance and characteristic numbers, Comm. Math. Phys. 174 (1995) 29 MR1372798 20 K Liu, Modular forms and topology, from: "Moonshine, the Monster, and related topics" (editors C Dong, G Mason), Contemp. Math. 193, Amer. Math. Soc. (1996) 237 MR1372725 21 J Lott, Higher-degree analogs of the determinant line bundle, Comm. Math. Phys. 230 (2002) 41 MR1930571 22 X Ma, W Zhang, Eta-invariants, torsion forms and flat vector bundles, Math. Ann. 340 (2008) 569 MR2357997 23 D Quillen, Determinants of Cauchy–Riemann operators on Riemann surfaces, Funktsional. Anal. i Prilozhen. 19 (1985) 37, 96 MR783704 24 E Witten, Global gravitational anomalies, Comm. Math. Phys. 100 (1985) 197 MR804460 25 W Zhang, Lectures on Chern–Weil theory and Witten deformations, Nankai Tracts in Mathematics 4, World Scientific Publishing Co. (2001) MR1864735