**Time and place:** MWF 12-1, Room 2-255

**Professor:** Jacob Lurie

**Office:** 2-271

**Office hours:** Monday 1-2 (or by appointment).

The
course
syllabus.

**Lectures**:
Lecture 1: Overview.

Lecture 3: Whitehead Triangulations.

Lecture 4: Existence of Triangulations.

Lecture 5: Uniqueness of Triangulations.

Lecture 6: Classifying Spaces of Manifolds.

Lecture 7: Triangulations in Families.

Lecture 8: Smooth vs. PL fiber bundles.

Lecture 9: An Engulfing Argument.

Lecture 10: PL vs. Smooth fiber bundles.

Lecture 11: Microbundles and Homotopies.

Lecture 12: Classifying Spaces for Microbundles.

Lecture 13: Homeomorphisms vs. Embeddings.

Lecture 14: The Kister-Mazur Theorem.

Lecture 15: Microbundles and Smoothing.

Lecture 17: Classification of Smooth Structures.

Lecture 18: Product Structure Theorems.

Lecture 19: Proof of the Product Structure Theorem: First Reductions.

Lecture 20: Proof of the Product Structure Theorem: Isolating Singularities.

Lecture 21: Proof of the Product Structure Theorem: Inductive Step.

Lecture 22: Proof of the Product Structure Theorem: Final Steps.

Lecture 23: Smooth vs. PL Structures.

Lecture 24: Diffeomorphisms of the 2-Sphere.

Lecture 25: Prime Decomposition of 3-Manifolds.

Lecture 26: Uniqueness of Prime Decompositions.

Lecture 27: Irreducibility and 2-Spheres.

Lecture 28: The Loop Theorem: Reduction to a Special Case.

Lecture 29: The Loop Theorem: Special Case.

Lecture 30: The Sphere Theorem: Part I.

Lecture 31: The Sphere Theorem: Part II.

Lecture 32: Incompressible Surfaces.

Lecture 33: Classification of Surfaces.

Lecture 34: Geometric Structures on Surfaces.

Lecture 36: Mapping Class Groups.

Lecture 37: More on Mapping Class Groups.

Lecture 38: The Dehn-Nielsen Theorem.

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