Topics in Analysis: Smooth Operator Algebras and K-theory

I invite questions about, corrections of and comments on these notes --
I am interested to hear about even minor errors, typos, stupidities, etc.

• Bkly08.pdf
  Cumulative Lecture notes.
• Front.pdf
  
• Section1.pdf
  Lecture 1: Wedneday, 27 August -- The smoothing group.
• Section2.pdf
  Lecture 2: Friday, 29 August -- Finite rank approximation.
  
• Section3.pdf
  Lecture 3: Wednesday, 3 September -- K-groups and loop groups.
• Section4.pdf
  Lecture 4: Friday, 5 September -- Delooping and Chern forms.
• Section5.pdf
  Lecture 5: Monday, 8 September -- Harmonic oscillator.
• Section6.pdf
  Lecture 6: Wednesday, 10 September -- Higher loop groups and determinant.
• Section7.pdf
  Topic 1: In place of lecture for Friday, 12 September -- Determinant and eta.
• Section8.pdf
  Topic 2: In place of lecture for Monday, 15 September -- Higher dimensional harmonic oscillator.
• Section9.pdf
  Topic 3: In place of lecture for Wednesday, 17 September -- Clifford algebras.
• Section10.pdf
  Lecture 7: Friday, 19 September -- Semiclassical quantization.
• Section11.pdf
  Lecture 8: Monday, 22 September -- Bott element.
• Section12.pdf
  Lecture 9: Wednesday, 24 September -- Adiabatic algebra and group.
• Section13.pdf
  Lecture 10: Friday, 26 September -- Bott periodicity.
• Section14.pdf
  Lecture 11: Monday, 29 September -- Adiabatic periodicity map.
• Section15.pdf
  Lecture 12: Wednesday, 1 October -- Atiyah's rotation.
• Section16.pdf
  Lecture 13: Friday, 3 October -- Involutions and K⁰.
• Section17.pdf
  Lecture 14: Monday, 6 October -- Even periodicity map.
• Section18.pdf
  Lecture 15: Wednesday, 8 October -- Vector bundles and K⁰.
• Section19.pdf
  Lecture 16: Friday, 10 October -- The Chern Character.
• Section20.pdf
  Lecture 17: Monday, 13 October -- Isotropic calculus and looping sequence.
• Section21.pdf
  Lecture 18: Wednesday, 15 October -- The determinant bundle.
• Section22.pdf
  Lecture 19: Friday, 17 October -- Riesz regularization.
• Section23.pdf
  Lecture 20: Monday, 20 October -- Trace defect formula.
• Section24.pdf
  Lecture 21: Wednesday, 22 October -- Curvature and Chern class.
• Section25.pdf
  Lecture 22: Friday, 24 October -- Isotropic families index (k=1).
• Section26.pdf
  Lecture 23: Monday, 27 October -- Iterated periodicity maps.
• Section27.pdf
  Lecture 24: Wednesday, 29 October -- Thom isomorphism.
• Section28.pdf
  Lecture 25: Friday, 31 October -- Isotropic families index theorem.
• Section29.pdf
  Lecture 26: Monday, 3 November -- Semiclassical push-forward for fibrations.
• Section30.pdf
  Lecture 27: Wednesday, 5 November -- Analytic index of Atiyah and Singer.
• Section31.pdf
  Lecture 28: Friday, 7 November -- Relative and compactly-supported K-theory.
• Section32.pdf
  Lecture 29: Monday, 10 November -- Toeplitz operators and the semiclassical limit
• Section33.pdf
  Lecture 30: Wednesday, 12 November -- Topological index
• Section34.pdf
  Lecture 31: Friday, 14 November -- Iterated fibrations and Multiplicativity
• Section35.pdf
  Topic 4: In place of lecture for Monday, 18 November -- Thom isomorphism and the Todd class
• Section36.pdf
  Topic 5: In place of lecture for Wednesday, 20 November -- Atiyah-Hirzebruch theorem
• Section37.pdf
  Topic 6: In place of lecture for Friday, 22 November -- The Atiyah-Singer index formula
• Section38.pdf
  Topic 7: In place of lecture for Monday, 25 November -- Product-type pseudodifferential operators
• Section39.pdf
  Topic 8: In place of lecture for Wednesday, 27 November -- More on the determinant bundle
• Section40.pdf
  Topic 9: In place of lecture for Friday, 29 November -- K-homology
• Section41.pdf
  Lecture 32: Monday, 1 December -- The K-theory gerbe
• Section42.pdf
  Lecture 33: Wednesday, 3 December -- The B-field
• Section43.pdf
  Lecture 34: Friday, 5 December -- Gerbe data
• Section44.pdf
  Lecture 35: Monday, 8 December -- The K-theory 2-gerbe
• Section44.pdf
  Lecture 36: Wednesday, 10 December -- Push-forward and torsion twisting
• Rear.pdf
  References