Spectral triples for pseudomanifolds with isolated singularity;Triplets spectraux pour les variétés à singularité conique isolée

Bulletin de la Societe Mathematique de France

Volumn 129, Issue 4, 2001, Pages 593-623

  Lescure, Jean Marie ^a  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042913572     PISSN: 00379484     EISSN: None     Source Type: Journal    
DOI: 10.24033/bsmf.2409     Document Type: Article

References (29)

1. BAUM (P.) & DOUGLAS (R.) - K-homology and index theory, Proc. Sympos. Pure Math., t. 38 (1982), no. 1, pp. 117-173.
2. BERLINE (N.), GETZLER (E.) & VERGNE (M.) - Heat kernels and Dirac operators, Comprehensive Studies in Math., vol. 298, Springer-Verlag, 1991.
3. BOST (J.B.) - Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs, Invent. Math., t. 101 (1990), pp. 261-333.
4. BRÜNING (J.) & LESCH (M.) - On the spectral geometry of algebraic curves, J. reine angew Math., t. 474 (1996), pp. 25-66.
5. BRÜNING (J.) & SEELEY (R.) - Regular singular asymptotics, Advances in Math., t, 58 (1985), pp. 133-148.
6. _, An index theorem for first order regular singular operators, Amer. J. Math., t. 110 (1988), pp. 659-714.
7. CHAN (S.W.) - Periodic cyclic cohomology Chern character for pseudomanifolds with one singular stratum, Proc. AMS, t. 126 (1998), 110, 3, pp. 669-675.
8. CHEEGER (J.) - On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. USA, t. 76 (1979), pp. 2103-2106.
9. _, Spectral geometry of singular riemannian spaces, J. Diff. Geom., t. 18 (1983), pp. 575-657.
10. CHOU (A.W.) - The Dirac operator on spaces with conical singularities and positive scalar curvatures, Trans. AMS, t. 289 (1985), no. 1, pp. 1-40.
11. CONNES (A.) - Noncommutative differential geometry, Pub. IHES, t. 62 (1985), pp. 257-360.
12. _, Noncommutative Geometry, Academic Press, 1994.
13. CONNES (A.) & MOSCOVICI (H.) - Cyclic cohomology, Novikov conjecture and hyperbolic groups, Topology, t. 29 (1990), pp. 345-388.
14. _, The local index formula in noncommutative geometry, GAFA, t. 5 (1995), no. 2, pp. 174-243.
15. CUNTZ (J.) & QUILLEN (R.) - On excision in periodic cyclic cohomology II : the general case, C.R. Acad Sc. Paris Série I, t. 318 (1994), pp. 11-12.
16. GETZLER (E.) - Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem, Commun. Math. Phys., t. 92 (1983), pp. 163-178.
17. GRUBB (G.) & SEELEY (R.) - Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems, Invent. Math., t. 121 (1995), no. 3, pp. 481-529.
18. JAFFE (A.), LESNIEWSKI (A.) & OSTERWALDER (K.) - Quantum K-theory I. The Chern character, Commun. Math. Phy., t. 118 (1988), pp. 1-14.
19. KASPAROV (G.G.) - Equivariant KK-theory and the Novikov conjecture, Invent. Math., t. 91 (1988), pp. 147-201.
20. LAWSON (H.) & MICHELSOHN (M.L.) - Spin geometry, Princeton Math. Series, vol. 38, Princeton University Press, Princeton, New Jersey, 1989.
21. LESCH (M.) - Deficiency indices for symmetric Dirac operators on manifolds with conic singularities, Topology, t. 32 (1993), no. 3, pp. 611-623.
22. _, Operators of Fuchs type, conical singularities, and asymptotic methods, B. G. Teubner Verlagsgesellschaft mbH, Stuttgart, 1997.
23. LESCURE (J.-M.) - Triplets spectraux pour les pseudovariétés à singularité conique, isolée, Thèse de Doctorat, Université P. Sabatier, 1998.
24. MELROSE (R.B.) - The Atiyah-Patodi-Singer index theorem, Research Notes in Math., vol. 4, A. K. Peters, Massachusetts, 1993.
25. MOSCOVICI (H.) & WU (F.) - Straight Chern character for Witt spaces, preprint IHES, 1996.
26. DE RHAM (G.) - Variétés différentiates, Publ. math. Univ. Nancago, vol. Actualités scient. indus., 1222, Hermann, Paris, trois. ed. 1973.
27. SCHULZE (B. W.) - Boundary value problems and singular pseudodifferential operators, Wiley-Intersciences, 1998.
28. SHUBIN (M.A.) - Pseudodifferential operators and spectral theory, Springer Verlag, 1980.
29. SKANDALIS (G.) - Kasparov's bivariant K-theory and applications, Expositiones Math., t. 9 (1991), pp. 193-250.