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Volumn 241, Issue 2-3, 2003, Pages 215-234

A New Short Proof of the Local Index Formula and Some of Its Applications

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EID: 0242339396     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0915-4     Document Type: Article
Times cited : (32)

References (30)
  • 1
    • 0000243409 scopus 로고
    • On the heat equation and the index theorem
    • [ABP]
    • [ABP] Atiyah, M., Bott, R., Patodi. V.: On the heat equation and the index theorem. Invent. Math. 19, 279-330 (1973)
    • (1973) Invent. Math. , vol.19 , pp. 279-330
    • Atiyah, M.1    Bott, R.2    Patodi, V.3
  • 2
    • 0001579635 scopus 로고
    • The index of elliptic operators. I
    • [AS1]
    • [AS1] Atiyah, M., Singer, I.: The index of elliptic operators. I. Ann. of Math. (2) 87, 484-530 (1968)
    • (1968) Ann. of Math. (2) , vol.87 , pp. 484-530
    • Atiyah, M.1    Singer, I.2
  • 3
    • 0001579635 scopus 로고
    • The index of elliptic operators. III
    • [AS2]
    • [AS2] Atiyah, M., Singer, I.: The index of elliptic operators. III. Ann. of Math. (2) 87, 546-604 (1968)
    • (1968) Ann. of Math. (2) , vol.87 , pp. 546-604
    • Atiyah, M.1    Singer, I.2
  • 6
    • 84972510766 scopus 로고
    • The heat equation on a CR manifold
    • [BGS]
    • [BGS] Beals, R., Greiner, P., Stanton, N.: The heat equation on a CR manifold. J. Differ. Geom. 20, 343-387 (1984)
    • (1984) J. Differ. Geom. , vol.20 , pp. 343-387
    • Beals, R.1    Greiner, P.2    Stanton, N.3
  • 8
    • 0002876396 scopus 로고
    • The Atiyah-Singer theorems: A probabilistic approach. I. The index theorem
    • [Bi]
    • [Bi] Bismut, J.-M.: The Atiyah-Singer theorems: A probabilistic approach. I. The index theorem. J. Fund. Anal. 57, 56-99 (1984)
    • (1984) J. Fund. Anal. , vol.57 , pp. 56-99
    • Bismut, J.-M.1
  • 9
    • 33744647630 scopus 로고
    • The analysis of elliptic families
    • [BF]
    • [BF] Bismut, J.-M., Freed, D.: The analysis of elliptic families. Commun. Math. Phys 107, 103-163 (1986)
    • (1986) Commun. Math. Phys , vol.107 , pp. 103-163
    • Bismut, J.-M.1    Freed, D.2
  • 10
    • 0039462551 scopus 로고    scopus 로고
    • Equivariant Chern character for the invariant Dirac operator
    • [CH]
    • [CH] Chern, S., Hu, X.: Equivariant Chern character for the invariant Dirac operator. Michigan Math. J. 44, 451-473 (1997)
    • (1997) Michigan Math. J. , vol.44 , pp. 451-473
    • Chern, S.1    Hu, X.2
  • 11
  • 12
    • 0000151581 scopus 로고
    • The local index formula in noncommutative geometry
    • [CM1]
    • [CM1] Connes, A., Moscovici, H.: The local index formula in noncommutative geometry. GAFA 5, 174-243 (1995)
    • (1995) GAFA , vol.5 , pp. 174-243
    • Connes, A.1    Moscovici, H.2
  • 13
    • 0003794206 scopus 로고
    • Schrödinger operators with application to quantum mechanics and global geometry
    • [CFKS]. Berlin-Heidelberg-New York: Springer-Verlag
    • [CFKS] Cycon, H., Froese, R., Kirsch, W., Simon, B.: Schrödinger operators with application to quantum mechanics and global geometry. Texts and Monographs in Physics. Berlin-Heidelberg-New York: Springer-Verlag, 1987
    • (1987) Texts and Monographs in Physics
    • Cycon, H.1    Froese, R.2    Kirsch, W.3    Simon, B.4
  • 14
    • 0003350969 scopus 로고
    • Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
    • [Ge1]
    • [Ge1] Getzler, E.: Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem. Commun. Math. Phys. 92, 163-178 (1983)
    • (1983) Commun. Math. Phys. , vol.92 , pp. 163-178
    • Getzler, E.1
  • 15
    • 0002846281 scopus 로고
    • A short proof of the local Atiyah-Singer index theorem
    • [Ge2]
    • [Ge2] Getzler, E.: A short proof of the local Atiyah-Singer index theorem. Topology 25, 111-117 (1986)
    • (1986) Topology , vol.25 , pp. 111-117
    • Getzler, E.1
  • 16
    • 0000751768 scopus 로고
    • The odd Chern character in cyclic homology and spectral flow
    • [Ge3]
    • [Ge3] Getzler, E.: The odd Chern character in cyclic homology and spectral flow. Topology 32, 489-507 (1993)
    • (1993) Topology , vol.32 , pp. 489-507
    • Getzler, E.1
  • 19
    • 0000724778 scopus 로고
    • An asymptotic expansion for the heat equation
    • [Gr]
    • [Gr] Greiner, P.: An asymptotic expansion for the heat equation. Arch. Rational Mech. Anal. 41, 163-218 (1971)
    • (1971) Arch. Rational Mech. Anal. , vol.41 , pp. 163-218
    • Greiner, P.1
  • 20
    • 0000028732 scopus 로고
    • A new proof of Weyl's formula on the asymptotic distribution of eigenvalues
    • [Gu]
    • [Gu] Guillemin, V.: A new proof of Weyl's formula on the asymptotic distribution of eigenvalues. Adv. in Math. 55, 131-160 (1985)
    • (1985) Adv. in Math. , vol.55 , pp. 131-160
    • Guillemin, V.1
  • 23
    • 0042913572 scopus 로고    scopus 로고
    • Triplets spectraux pour les variétés à singularité conique isolée
    • [Le]
    • [Le] Lescure, J.-M.: Triplets spectraux pour les variétés à singularité conique isolée. Bull. Soc. Math. France 129, 593-623 (2001)
    • (2001) Bull. Soc. Math. France , vol.129 , pp. 593-623
    • Lescure, J.-M.1
  • 26
    • 0031492814 scopus 로고    scopus 로고
    • Eigenvalue inequalities and Poincaré duality in noncommutative geometry
    • [Mo]
    • [Mo] Moscovici, H.: Eigenvalue inequalities and Poincaré duality in noncommutative geometry. Commun. Math. Phys. 184, 619-628 (1997)
    • (1997) Commun. Math. Phys. , vol.184 , pp. 619-628
    • Moscovici, H.1
  • 27
    • 0002106203 scopus 로고
    • Une classe d'opérateurs pseudo-différentiels du type de Volterra
    • [Pi]
    • [Pi] Piriou, A.: Une classe d'opérateurs pseudo-différentiels du type de Volterra. Ann. Inst. Fourier 20, 77-94 (1970)
    • (1970) Ann. Inst. Fourier , vol.20 , pp. 77-94
    • Piriou, A.1
  • 28
    • 0004065705 scopus 로고    scopus 로고
    • Elliptic operators, topology and asymptotic methods
    • [Ro], New York: Longman
    • [Ro] Roe, J.: Elliptic operators, topology and asymptotic methods. Pitman Research Notes in Math-ematics Series 395, New York: Longman, 1998
    • (1998) Pitman Research Notes in Math-ematics Series
    • Roe, J.1
  • 29
    • 0003278080 scopus 로고    scopus 로고
    • Partial differential equations. II
    • [Ta], Berlin-Heidelberg-New York: Springer-Verlag
    • [Ta] Taylor, M.E.: Partial differential equations. II. Applied Mathematical Sciences, 116, Berlin-Heidelberg-New York: Springer-Verlag, 1996
    • (1996) Applied Mathematical Sciences , vol.116
    • Taylor, M.E.1
  • 30
    • 0002794818 scopus 로고
    • Local invariants of spectral asymmetry
    • [Wo]
    • [Wo] Wodzicki, M.: Local invariants of spectral asymmetry. Invent. Math. 75, 143-177 (1984)
    • (1984) Invent. Math. , vol.75 , pp. 143-177
    • Wodzicki, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.