Algebraic K-Theory and Manifold Topology
(Math 281)
|
Time and place: MWF 12-1, Science Center 310
Professor: Jacob Lurie
|
| The
|
course
syllabus. |
Lecture Notes:
| Lecture 1:
|
Overview. |
| Lecture 2:
|
The Wall Finiteness
Obstruction. |
| Lecture 3:
|
Whitehead Torsion: Part I. |
| Lecture 4:
|
Whitehead Torsion: Part
II. |
| Lecture 5:
|
Cell-Like Maps. |
| Lecture 6:
|
Concordance of
Polyhedra. |
| Lecture 7:
|
Higher Simple Homotopy
Theory. |
| Lecture 8:
|
Fibrations of Polyhedra. |
| Lecture 9:
|
Fibrations of
Nonsingular Simplicial Sets. |
| Lecture 10:
|
Combinatorial Models for
Simple Homotopy Theory. |
| Lecture 11:
|
Equivalence of the
Combinatorial Definition. |
| Lecture 12:
|
Some Loose Ends. |
| Lecture 13:
|
Homotopy Types vs Simple
Homotopy Types. |
| Lecture 14:
|
(Lower) K-Theory
of infty-Categories. |
| Lecture 15:
|
The Wall Finiteness
Obstruction Revisited. |
| Lecture 16:
|
Higher K-Theory of
infty-Categories. |
| Lecture 17:
|
The Additivity Theorem. |
| Lecture 18:
|
Additive K-Theory. |
| Lecture 19:
|
K-Theory of Ring Spectra. |
| Lecture 20:
|
Lower K-Groups of Ring
Spectra. |
| Lecture 21:
|
The Algebraic K-Theory of
Spaces. |
| Lecture 22:
|
Constructible
Sheaves. |
| Lecture 23:
|
Universal Local Acyclicity. |
| Lecture 24:
|
The Assembly Map. |
| Lecture 25:
|
The Assembly Map II. |
| Lecture 26:
|
The Assembly Map III. |
| Lecture 27:
|
Higher Torsion. |
| Lecture 28:
|
Another Assembly Map. |
| Lecture 29:
|
Another Assembly Map II. |
| Lecture 30:
|
The Whitehead Space. |
| Lecture 31:
|
The Whitehead Space II. |
| Lecture 32:
|
Proof of the Main
Theorem. |
| Lecture 33:
|
Digression: Review of
Microbundles |
| Lecture 34:
|
Overview of Part 3 |
| Lecture 35:
|
The Setup |
| Lecture 36:
|
The Combinatorial Step
(Part I) |
| Lecture 37:
|
The Combinatorial Step
(Part II) |
| Lecture 38:
|
Thickenings of a
Point |
Back to Jacob Lurie's home page.