Algebraic L-theory and Surgery (287x) Algebraic L-theory and Surgery (287x)

Time and place: MWF 1-2, TBA

Professor: Jacob Lurie
Office: Science Center 435
Office hours: Thursday 2-3 (or by appointment).
The course syllabus.

Lectures (Warning: these notes are sloppy. Use at own risk.): Lecture 1: Introduction.

Lecture 2: Categorical Background.

Lecture 3: Stable Infty Categories.

Lecture 4: Quadratic Functors.

Lecture 5: L Groups.

Lecture 6: L Theory Spaces.

Lecture 7: Simplicial Spaces.

Lecture 8: Localization.

Lecture 9: Proof of the Kan Property.

Lecture 10: L-Theory of Rings and Ring Spectra.

Lecture 11: Algebraic Surgery.

Lecture 12: Surgery below the Middle Dimension.

Lecture 13: The L-theory of Fields.

Lecture 15: Odd L-groups of Z.

Lecture 16: Even L-groups of Z.

Lecture 17: Polyhedra and PL Manifolds.

Lecture 18: Constructible Sheaves.

Lecture 19: Verdier Duality.

Lecture 20: L-Theory Spectra.

Lecture 21: Locally Constant Sheaves.

Lecture 22: Assembly.

Lecture 23: Orientation of L-Theory.

Lecture 24: More on L-Theory Orientations.

Lecture 25: The Hirzebruch Signature Formula.

Lecture 26: Poincare Spaces.

Lecture 27: The Structure Space of a Poincare Space.

Lecture 28: Transversality.

Lecture 29: Quadratic Refinements.

Lecture 30: The Main Theorem.

Lecture 31: The Main Theorem: First Reductions.

Lecture 32: Surgery.

Lecture 33: From Algebraic To Geometric Surgery.

Lecture 34: Geometric Surgery Below the Middle Dimension.

Lecture 35: Surgery in the Middle Dimension.

Lecture 36: The Homotopy Type of G/PL.

Lecture 37: The Total Surgery Obstruction.

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