Determinant lines, von Neumann algebras and L2 torsion

Journal fur die Reine und Angewandte Mathematik

Volumn 484, Issue , 1997, Pages 153-181

  Carey, A ^a   Farber, M ^b   Mathai, V ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031484327     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. [ASS] H. Araki, M.-S. B. Smith and L. Smith, On the homotopical significance of the type of von Neumann algebra factors, Comm. Math. Phys. 22 (1971), 71-88.
2. [BGS] J.M. Bismut, H. Gillet, C. Soule, Analytic torsion and holomorphic determinant bundles, I, II, III, Comm. Math. Phys. 115 (1988), 49-78; 115 (1988), 79-126; 115 (1988), 301-351.
3. [BGS] J.M. Bismut, H. Gillet, C. Soule, Analytic torsion and holomorphic determinant bundles, I, II, III, Comm. Math. Phys. 115 (1988), 49-78; 115 (1988), 79-126; 115 (1988), 301-351.
4. [BGS] J.M. Bismut, H. Gillet, C. Soule, Analytic torsion and holomorphic determinant bundles, I, II, III, Comm. Math. Phys. 115 (1988), 49-78; 115 (1988), 79-126; 115 (1988), 301-351.
5. [BZ] J.-M. Bismut, W. Zhang, An extension of a theorem by Cheeger and Muller, Astérisque 205 (1992).
6. [Br] M. Breiter, Theory of Fredholm operators and vector bundles relative to a von Neumann algebra, Rocky Mountain J. Math. 3 (1973), 383-427.
7. [BFKM] D. Burghelea, L. Friedlander, T. Kappeler and P. McDonald, Analytic and Reidemeister torsion for representations in finite type Hilbert modules, GAFA 6:5 (1996).
8. 2-torsion invariants, J. Funct. Anal. 110 (1992), 377-409.
9. [Di] J. Dixmier, Von Neumann algebras, North-Holland, Amsterdam 1981.
10. 2 cohomology of infinite coverings, Topology 16 (1977), 157-165.
11. [E] A. V. Efremov, Combinatorial and analytic Novikov-Shubin invariants, Russ. Math. Surv. 46 (1991), 219-220.
12. [F] M. Farber, Combinatorial invariants computing the Ray-Singer analytic torsion, Diff. Geom. Appl. 6 (1996), 351-366.
13. [F1] M. Farber, Abelian categories, Novikov-Shubin invariants, and Morse inequalities, C. R. Acad. Sei. Paris 321 (1955), 1953-1995.
14. [F2] M. Farber, Homological Algebra of Novikov-Shubin invariants and Morse inequalities, GAFA 6:4 (1996), 628-665.
15. [F3] M. Farber, Singularities of analytic torsion, J. Diff. Geom. 41 (1995), 528-572.
16. [FK] B. Fuglede and R. V. Kadison, Determinant theory in finite factors, Ann. Math. 55 (1952), 520-530.
17. [GS] M. Gromov and M. Shubin, Von Neumann spectra near zero, GAFA 1 (1991), 375-404.
18. [HS] P. de la Harpe, G. Skandalis, Déterminant associé àune trace sur une algèbre de Banach, Ann. Inst. Fourier, Grenoble 34 (1984), 241-260.
19. [La] S. Lang, Introduction to differentiable manifolds, Interscience, 1962.
20. [L] J. Lott, Heat kernels on covering spaces and topological invariants, J. Diff. Geom. 35 (1992), 471-510.
21. 2-topological invariants of manifolds, Inv. Math. (1995).
22. 2-torsion and 3-manifolds, Low-dimensional Topology (Knoxville, TN, 1992) Conf. Proc. (1994), Internat. Press, Cambridge, MA, 75-107.
23. [LR] W. Lück, M. Rothenberg, Reidemeister torsion and the K-theory of von Neumann algebras, K-Theory 5 (1991), 213-264.
24. [Luk] G. Luke, Pseudodifferential operators on Hilbert bundles, J. Diff. Equ. 12 (1972), 566-589.
25. 2-analytic torsion, J. Funct. Anal. 107 (1992), 369-386.
26. [Mi1] J. Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. Math. 74 (1961), 575-590.
27. [Mi2] J. Milnor, A duality theorem for Reidemeister torsion, Ann. Math. 76 (1962), 137-147.
28. [Mi3] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426.
29. [Mu] W. Müller, Analytic torsion and R-torsion for unimodular representations, J. Amer. Math. Soc. 6 (1993), 721-743.
30. [RS] D. B. Ray and I.M. Singer, R-torsion and the Laplacian on Riemannian manifolds. Adv. Math. 7 (1971), 145-210.