Algebraic K-Theory and Manifold Topology (Math 281) 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

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