Some conformal invariants from the noncommutative residue for manifolds with boundary

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Volumn 3, Issue , 2007, Pages

  Ugalde, William J ^a  

^a UNIVERSIDAD DE COSTA RICA   (Costa Rica)

Author keywords

Conformal invariants; Fredholm module; Manifolds with boundary; Noncommutative residue

Indexed keywords

EID: 84889234585     PISSN: None     EISSN: 18150659     Source Type: Journal    
DOI: 10.3842/SIGMA.2007.104     Document Type: Article

References (24)

1. Adler M., On a trace functional for formal pseudodifferential operators and the symplectic structure of the Korteweg-de Vries type equations, Invent. Math. 50 (1979), 219-248.
2. Bär C., Conformal structures in noncommutative geometry, J. Noncommut. Geom. 1 (2007), 385-395, arXiv:0704.2119.
3. Boutet de Monvel L., Boundary problems for pseudo-differential operators, Acta Math. 126 (1971), 11-51.
4. Connes A., The action functional in noncommutative-geometry, Comm. Math. Phys. 117 (1988), 673-683.
5. Connes A., Quantized calculus and applications, in Proceedings of the XIth International Congress of Mathematical Physics, International Press, Cambridge, MA, 1995, 15-36.
6. Connes A., Noncommutative geometry, Academic Press, London and San Diego, 1994.
7. Connes A., Sullivan D., Teleman N., Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes, Topology 33 (1994), 663-681.
8. Fedosov B.V., Golse F., Leichtnam E., Schrohe E., The noncommutative residue for manifolds with boundary, J. Funct. Anal. 142 1996, 1-31.
9. Gracia-Bondía J.M., Várilly J.C., Figueroa H. Elements of noncommutative geometry, Birkhäuser Advanced Texts, Birkhäuser, Boston, 2001.
10. Graham R., Jenne R., Mason L., Sparling G., Conformally invariant powers of the Laplacian. I. Existence, J. London Math. Soc. (2) 46 (1992), 557-565.
11. Grubb G., Singular Green operators and their spectral asymptotics, Duke Math. J. 51 (1984), 477-528.
12. Guillemin V.W., A new proof of Weyl's formula on the asymptotic distribution of eigenvalues, Adv. Math. 55 (1985), 131-160.
13. Manin Yu.I., Algebraic aspects of nonlinear differential equations, J. Sov. Math. 11 (1979), 1-22.
14. Paneitz S., A quadratic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds, Preprint, 1983.
15. Polyakov A., Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981), 207-210.
16. Polyakov A., Quantum geometry of fermionic strings, Phys. Lett. B 103 (1981), 211-213.
17. Schrohe E., Noncommutative residue, Dixmier's traces, and heat trace expansions on manifolds with boundary, Contemp. Math. 242 (1999), 161-186, math.AP/9911053.
18. Schrohe E., A short introduction to Boutet de Monvel's calculus, in Approaches to Singular Analysis, Editors J. Gil, D. Grieser and M. Lesch, Birkhäuser, Basel, 2001, 85-116.
19. Ugalde W.J., Differential forms canonically associated to even-dimensional compact conformal manifolds, in Clifford Algebras. Applications to Mathematics, Physics, and Engineering, Editor R. Ablamowicz, Progress in Mathematical Physics, Vol. 34, Birkhäuser, Boston, 2004, 211-225, math.DG/0211240.
20. Ugalde W.J., A construction of critical GJMS operators using Wodzicki's residue, Comm. Math. Phys. 261 (2006), 771-788, math.DG/0403392.
21. Ugalde W.J., Differential forms and the Wodzicki residue, math.DG/0211361.
22. Wang Y., Differential forms and the Wodzicki residue for manifolds with boundary, J. Geom. Phys. 56 (2006), 731-753, math.DG/0609062.
23. Wang Y., Differential forms and the noncommutative residue for manifolds with boundary in the non-product case, Lett. Math. Phys. 77 (2006), 41-51, math.DG/0609060.
24. Wodzicki M., Local invariants of spectral asymmetry, Invent. Math. 75 (1984), 143-178.