Topics in Analysis: Smooth Operator Algebras and Ktheory
Lectures at Berkeley, Fall 2008
Lecture notes: Last changed 6 February, 2009
Lecture 1 revised; version 0.5L
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  Kgroups 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 K^{0}.

Section17.pdf
Lecture 14: Monday, 6 October  Even periodicity map.

Section18.pdf
Lecture 15: Wednesday, 8 October  Vector bundles and K^{0}.

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 pushforward for fibrations.

Section30.pdf
Lecture 27: Wednesday, 5 November  Analytic index of Atiyah and Singer.

Section31.pdf
Lecture 28: Friday, 7 November  Relative and compactlysupported Ktheory.

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 
AtiyahHirzebruch theorem

Section37.pdf
Topic 6: In place of lecture for Friday, 22 November 
The AtiyahSinger index formula

Section38.pdf
Topic 7: In place of lecture for Monday, 25 November 
Producttype 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 
Khomology

Section41.pdf
Lecture 32: Monday, 1 December  The Ktheory gerbe

Section42.pdf
Lecture 33: Wednesday, 3 December  The Bfield

Section43.pdf
Lecture 34: Friday, 5 December  Gerbe data

Section44.pdf
Lecture 35: Monday, 8 December  The Ktheory 2gerbe

Section44.pdf
Lecture 36: Wednesday, 10 December  Pushforward and torsion twisting

Rear.pdf
References