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Volumn 5, Issue 4, 1999, Pages 467-506

The index of elliptic operators on manifolds with conical points

Author keywords

Elliptic operators; Index; Manifolds with singularities; Pseudodifferential operators

Indexed keywords


EID: 0039228970     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s000290050054     Document Type: Article
Times cited : (12)

References (46)
  • 1
    • 0000082083 scopus 로고
    • An abstract index theorem on non-compact Riemannian manifolds
    • [Ang93]
    • [Ang93] N. Anghel. An abstract index theorem on non-compact Riemannian manifolds. Houston J. Math. 19 (1993), 223-237.
    • (1993) Houston J. Math. , vol.19 , pp. 223-237
    • Anghel, N.1
  • 3
    • 0002766610 scopus 로고
    • Eta-invariants and their adiabatic limits
    • [BC89]
    • [BC89] M. Bismut and J. Cheeger. Eta-invariants and their adiabatic limits. J.A.M.S. 2 (1989), 33-70.
    • (1989) J.A.M.S. , vol.2 , pp. 33-70
    • Bismut, M.1    Cheeger, J.2
  • 4
    • 0010948076 scopus 로고
    • Families index for manifolds with boundary, superconnections and cones
    • [BC90]
    • [BC90] M. Bismut and J. Cheeger. Families index for manifolds with boundary, superconnections and cones. Invent. Math. 89 (1990), 91-151.
    • (1990) Invent. Math. , vol.89 , pp. 91-151
    • Bismut, M.1    Cheeger, J.2
  • 5
    • 50749133616 scopus 로고
    • Residues of the eta function for an operator of Dirac type
    • [BG92]
    • [BG92] Th. P. Branson and P. B. Gilkey. Residues of the eta function for an operator of Dirac type. J. Fund. Anal. 108 (1992), 47-87.
    • (1992) J. Fund. Anal. , vol.108 , pp. 47-87
    • Branson, T.P.1    Gilkey, P.B.2
  • 6
    • 84972491113 scopus 로고
    • 2-index theorems on certain complete manifolds
    • [Brü90]
    • 2-index theorems on certain complete manifolds. J. Differential Geom. 32 (1990), 491-532.
    • (1990) J. Differential Geom. , vol.32 , pp. 491-532
    • Brüning, J.1
  • 7
    • 0000388563 scopus 로고
    • An index theorem for first order regular singular operators
    • [BS88]
    • [BS88] J. Brüning and R. Seeley. An index theorem for first order regular singular operators. Amer. J. Math. 110 (1988), 659-714.
    • (1988) Amer. J. Math. , vol.110 , pp. 659-714
    • Brüning, J.1    Seeley, R.2
  • 8
    • 84972545480 scopus 로고
    • Spectral geometry of singular Riemannian spaces
    • [Che83]
    • [Che83] J. Cheeger. Spectral geometry of singular Riemannian spaces. J. Differential Geom. 18 (1983), 175-221.
    • (1983) J. Differential Geom. , vol.18 , pp. 175-221
    • Cheeger, J.1
  • 9
    • 84972526496 scopus 로고
    • Eta invariants, the adiabatic approximation and conical singularities
    • [Che87]
    • [Che87] J. Cheeger. Eta invariants, the adiabatic approximation and conical singularities. J. Differential Geom. 26 (1987), 175-221.
    • (1987) J. Differential Geom. , vol.26 , pp. 175-221
    • Cheeger, J.1
  • 10
    • 84966240705 scopus 로고
    • The Dirac operator on spaces with conical singularities and positive scalar curvatures
    • [Cho85]
    • [Cho85] A. W. Chou. The Dirac operator on spaces with conical singularities and positive scalar curvatures. Trans. Amer. Math. Soc. 289 (1985), 1-40.
    • (1985) Trans. Amer. Math. Soc. , vol.289 , pp. 1-40
    • Chou, A.W.1
  • 11
    • 0000585515 scopus 로고
    • 2-cohomology and index theorem for the Bergman metric
    • [DF83]
    • 2-cohomology and index theorem for the Bergman metric. Ann. of Math. 118 (1983), 593-618.
    • (1983) Ann. of Math. , vol.118 , pp. 593-618
    • Donnelly, H.1    Fefferman, C.2
  • 12
    • 0041490890 scopus 로고
    • Adiabatic limits of the eta-invariants. the odd-dimensional Atiyah-Patodi-Singer problem
    • [DW91]
    • [DW91] R. G. Douglas and K. P. Wojciechowski. Adiabatic limits of the eta-invariants. The odd-dimensional Atiyah-Patodi-Singer problem. Comm. Math. Phys. 142 (1991), 139-168.
    • (1991) Comm. Math. Phys. , vol.142 , pp. 139-168
    • Douglas, R.G.1    Wojciechowski, K.P.2
  • 13
    • 0038201567 scopus 로고
    • Analytic formulas for the index of elliptic operators
    • [Fed74]
    • [Fed74] B. V. Fedosov. Analytic formulas for the index of elliptic operators. Trans Moscow Math. Soc. 30 (1974), 159-241.
    • (1974) Trans Moscow Math. Soc. , vol.30 , pp. 159-241
    • Fedosov, B.V.1
  • 15
    • 0037526192 scopus 로고    scopus 로고
    • On the index of elliptic operators on a wedge
    • [FST96]
    • [FST96] B. V. Fedosov, B.-W. Schulze, and N. N. Tarkhanov. On the index of elliptic operators on a wedge. J. Funct. Anal. 157 (1998), 164-209.
    • (1998) J. Funct. Anal. , vol.157 , pp. 164-209
    • Fedosov, B.V.1    Schulze, B.-W.2    Tarkhanov, N.N.3
  • 17
    • 0346269380 scopus 로고
    • Cyclic homology and the Atiyah-Patodi-Singer index theorem
    • [Get93]
    • [Get93] E. Getzler. Cyclic homology and the Atiyah-Patodi-Singer index theorem. Contemp. Math. 148 (1993), 19-45.
    • (1993) Contemp. Math. , vol.148 , pp. 19-45
    • Getzler, E.1
  • 18
    • 84990623241 scopus 로고
    • The eta invariant for a class of elliptic boundary value problems
    • [GS83a]
    • [GS83a] P. B. Gilkey and L. Smith. The eta invariant for a class of elliptic boundary value problems. Comm. Pure Appl. Math. 36 (1983), 85-131.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 85-131
    • Gilkey, P.B.1    Smith, L.2
  • 19
    • 84972530309 scopus 로고
    • The twisted index problem for manifolds with boundary
    • [GS83b]
    • [GS83b] P. B. Gilkey and L. Smith. The twisted index problem for manifolds with boundary. J. Differential Geom. 18 (1983), 393-444.
    • (1983) J. Differential Geom. , vol.18 , pp. 393-444
    • Gilkey, P.B.1    Smith, L.2
  • 20
    • 84951610586 scopus 로고
    • Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
    • [GL83]
    • [GL83] M. Gromov and H. B. Lawson. Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Publ. Math. I.H.E.S. 58 (1983), 83-196.
    • (1983) Publ. Math. I.H.E.S. , vol.58 , pp. 83-196
    • Gromov, M.1    Lawson, H.B.2
  • 21
    • 0001525162 scopus 로고
    • Heat operator trace expansions and index for general Atiyah-Patodi-Singer boundary problems
    • [Gru92]
    • [Gru92] G. Grubb. Heat operator trace expansions and index for general Atiyah-Patodi-Singer boundary problems. Comm. Part. Diff. Equ. 17 (1992), 2031-2077.
    • (1992) Comm. Part. Diff. Equ. , vol.17 , pp. 2031-2077
    • Grubb, G.1
  • 22
    • 0040857929 scopus 로고
    • Weakly parametric pseudodifferential operators and AtiyahPatodi-Singer boundary problems
    • [GS95]
    • [GS95] G. Grubb and R. Seeley. Weakly parametric pseudodifferential operators and AtiyahPatodi-Singer boundary problems. Invent. Math. 121 (1995), 481-529.
    • (1995) Invent. Math. , vol.121 , pp. 481-529
    • Grubb, G.1    Seeley, R.2
  • 24
    • 0000730698 scopus 로고
    • η-invariants on manifolds with cylindrical ends
    • [KW93]
    • [KW93] S. Klimek and K. Wojciechowski. η-invariants on manifolds with cylindrical ends. Differential Geom. Appl. 3 (1993), 191-201.
    • (1993) Differential Geom. Appl. , vol.3 , pp. 191-201
    • Klimek, S.1    Wojciechowski, K.2
  • 26
    • 0000457677 scopus 로고
    • Higher eta-invariants
    • [Lot92]
    • [Lot92] J. Lott. Higher eta-invariants. K-Theory 6 (1992), 191-233.
    • (1992) K-Theory , vol.6 , pp. 191-233
    • Lott, J.1
  • 27
    • 0001110758 scopus 로고
    • Transformation of boundary problems
    • [Mel81]
    • [Mel81] R. B. Melrose. Transformation of boundary problems. Acta Math. 147 (1981), 149-236.
    • (1981) Acta Math. , vol.147 , pp. 149-236
    • Melrose, R.B.1
  • 29
    • 0042245546 scopus 로고
    • The eta invariant and families of pseudodifferential operators
    • [Mel95]
    • [Mel95] R. B. Melrose. The eta invariant and families of pseudodifferential operators. Math. Res. Letters'2 (1995), 541-561.
    • (1995) Math. Res. Letters' , vol.2 , pp. 541-561
    • Melrose, R.B.1
  • 32
    • 0032221696 scopus 로고    scopus 로고
    • K-theory of C*-algebras of 6-pseudodifferential operators
    • [MN96b]
    • [MN96b] R. B. Melrose and V. Nistor. K-theory of C*-algebras of 6-pseudodifferential operators. Geom. Fund. Anal. 8 (1998), no. 1, 88-122.
    • (1998) Geom. Fund. Anal. , vol.8 , Issue.1 , pp. 88-122
    • Melrose, R.B.1    Nistor, V.2
  • 34
    • 0007188175 scopus 로고
    • Manifolds with cusps of rank one, spectral theory and L2-index theorem
    • [MÜ187] Springer-Verlag, Berlin
    • [MÜ187] W. Müller. Manifolds with cusps of rank one, spectral theory and L2-index theorem. Lect. Notes Math., vol. 1244. Springer-Verlag, Berlin, 1987.
    • (1987) Lect. Notes Math. , vol.1244
    • Müller, W.1
  • 35
    • 84972537262 scopus 로고
    • Eta invariants and manifolds with boundary
    • [Mül94]
    • [Mül94] W. Müller. Eta invariants and manifolds with boundary. J. Diff. Geom. 40 (1994), 311-377.
    • (1994) J. Diff. Geom. , vol.40 , pp. 311-377
    • Müller, W.1
  • 36
    • 0013480879 scopus 로고
    • On the index of elliptic operators on manifolds with boundary
    • [Pia93]
    • [Pia93] P. Piazza. On the index of elliptic operators on manifolds with boundary. J. Funct. Anal. 117 (1993), 308-359.
    • (1993) J. Funct. Anal. , vol.117 , pp. 308-359
    • Piazza, P.1
  • 37
    • 52449085626 scopus 로고
    • On the index of pseudodifferential operators with isolated singularities in symbols
    • [PR90] Russian
    • [PR90] B. A. Plamenevskii and G. V. Rozenblum. On the index of pseudodifferential operators with isolated singularities in symbols. Algebra i Analiz 2 (1990), 165-188. (Russian)
    • (1990) Algebra i Analiz , vol.2 , pp. 165-188
    • Plamenevskii, B.A.1    Rozenblum, G.V.2
  • 38
    • 0041617653 scopus 로고
    • Pseudodifferential operators with discontinuous symbols: K-theory and index formulas
    • [PR92] Russian
    • [PR92] B. A. Plamenevskii and G. V. Rozenblum. Pseudodifferential operators with discontinuous symbols: K-theory and index formulas. Funkts. Analiz 26 (1992), 266-275. (Russian)
    • (1992) Funkts. Analiz , vol.26 , pp. 266-275
    • Plamenevskii, B.A.1    Rozenblum, G.V.2
  • 44
    • 0001012948 scopus 로고
    • 2-index theorems on locally symmetric spaces
    • [Ste89]
    • 2-index theorems on locally symmetric spaces. Invent. Math. 96 (1989), 231-282.
    • (1989) Invent. Math. , vol.96 , pp. 231-282
    • Stern, M.1
  • 45
    • 84972492898 scopus 로고
    • Eta invariants and Hermitian locally symmetric spaces
    • [Ste90]
    • [Ste90] M. Stern. Eta invariants and Hermitian locally symmetric spaces. J. Differential Geom. 31 (1990), 771-789.
    • (1990) J. Differential Geom. , vol.31 , pp. 771-789
    • Stern, M.1
  • 46
    • 33750432710 scopus 로고
    • The Chern character and the eta-invariant of the Dirac operator
    • [Wu93]
    • [Wu93] F. Wu. The Chern character and the eta-invariant of the Dirac operator. K-Theory 7 (1993), 145-174.
    • (1993) K-Theory , vol.7 , pp. 145-174
    • Wu, F.1


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