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Pseudo-differential operators, heat calculus and index theory of groupoids satisfying the Lauter-Nistor condition

By Bing Kwan So


In this thesis, we study singular pseudo-differential operators defined by groupoids\ud satisfying the Lauter-Nistor condition, by a method parallel to that of manifolds\ud with boundary and edge differential operators. The example of the Bruhat sphere\ud is studied in detail. In particular, we construct an extension to the calculus of\ud uniformly supported pseudo-differential operators that is analogous to the calculus\ud with bounds defined on manifolds with boundary. We derive a Fredholmness criterion\ud for operators on the Bruhat sphere, and prove that their parametrices up to compact\ud operators lie inside the extended calculus; we construct the heat kernel of perturbed\ud Laplacian operators; and prove an Atiyah-Singer type renormalized index formula\ud for perturbed Dirac operators on the Bruhat sphere using the heat kernel method

Topics: QA
OAI identifier: oai:wrap.warwick.ac.uk:3793

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  3. (2007). A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem. doi
  4. (1976). An invitation to C -algebras. doi
  5. (2001). Analysis of geometric operators on open manifolds: a groupoid approach. In Quantization of singular symplectic quotients, doi
  6. (1995). Bismut super-connections and the Chern characters for Dirac operators on foliated manifolds. K-Theory, doi
  7. (2004). Complex powers and non-compact manifolds. doi
  8. (1991). Elliptic theory of edge dierential operators. doi
  9. (2002). Fredholm perturbations of Dirac operators on manifolds with corners. manuscript http://www.math.binghamton.edu/paul/papers/LoyMel.pdf,
  10. (2003). From heat-operators to anomalies: a walk through various regularization techniques in mathematics and physics. Emmy Nother Lectures, http://math.univ-bpclermont.fr/ paycha/articles/Goettingenlectures.ps,
  11. (2005). General theory of Lie groupoids and Lie algebroids. doi
  12. (2000). Groupoids and integration of Lie algebroids. doi
  13. (1992). Heat kernels and Dirac operators. doi
  14. (2001). Holonomy groupoids of singular foliations. doi
  15. (2003). Integrability of Lie brackets. doi
  16. (1993). Large time behavior of the heat kernel: On a theorem of Chavel and Karp. doi
  17. (1994). Lectures on the geometry of Poisson Manifolds. doi
  18. (2002). Lie algebroids, homonomy and characteristic classes. doi
  19. (2002). Lie Group beyound an introduction. Birkhauser,
  20. (1993). Natural Operators in Dierential Geometry. doi
  21. (1994). Noncommuative geometry.
  22. (2005). On some examples of Poisson homology and cohomology - analytic and Lie theoretic approaches. Master's thesis, The University of Hong Kong, doi
  23. (1973). Orbits of families of vector and integrability of distributions. doi
  24. (1991). Partial dierential operator of Elliptic type.
  25. (1990). Poisson Lie groups, dressing transformations and Bruhat decompositions.
  26. (2002). Possion cohomology of SU(2) covariant necklace Poisson structures on doi
  27. (2000). Pseudo-dierential analysis on continuous groupoids.
  28. (1999). Pseudo-dierential calculus on manifolds with corners and groupoids. doi
  29. (2007). Pseudo-dierential operators on manifolds with a Lie structure at in doi
  30. (1999). Pseudodierential operators on dierential groupoids. doi
  31. (2004). Singular integral operators on non-compact manifolds and analysis on polyhedral domains. arXiv:math/0402322,
  32. (2006). Sobolev spaces on Lie manifolds and regularity for polyhedral domains. doi
  33. Spectra of elliptic operators on non-compact manifolds. doi
  34. (1983). The analysis of linear partial dierential operators 1. doi
  35. (1993). The Atiyah-Patodi-Singer index theorem. A K Peters, doi
  36. The resolvent parametrix of the general elliptic linear dierential operator: a closed form for the intrinsic symbol. doi
  37. (2007). Weighted Sobolev spaces on Lie manifolds and regularity for polyhedral domains. doi

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