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Browse materialsMIT 18.917 · Fall 2007

Topics in Algebraic Topology: The Sullivan Conjecture

Subjects: Algebra · Geometry · Mathematics

Art: Anonymous painter,15th century, Westerner and Arab practicing geometry 15th century manuscript, 15th… · Public domain

Instructor: Prof. Jacob Lurie
Term: Fall 2007
Level: Graduate
What's inside: 1 lecture note · 1 reading · 38 other files · 1 web page
Materials open: MIT OCW

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Source: MIT OpenCourseWare 18.917 Topics in Algebraic Topology: The Sullivan Conjecture, Fall 2007, Prof. Jacob Lurie — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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MIT OpenCourseWare, Prof. Jacob Lurie, 18.917 Topics in Algebraic Topology: The Sullivan Conjecture, Fall 2007.

License: CC BY-NC-SA 4.0 · Edition: Fall 2007 · Open the original course on OCW ↗

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Topics in Algebraic Topology: The Sullivan Conjecture

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Lecture 1: Introduction ( PDF )

Lecture 2: Steenrod operations ( PDF )

Lecture 3: Basic properties of Steenrod operations ( PDF )

Lecture 4: The Adem relations ( PDF )

Lecture 5: The Adem relations (cont.) ( PDF )

Lecture 6: Admissible monomials ( PDF )

Lecture 7: Free unstable modules ( PDF )

Lecture 8: A theorem of Gabriel-Kuhn-Popesco ( PDF )

Lecture 9: Injectivity of the cohomology of BV ( PDF )

Lecture 10: Generating analytic functors ( PDF )

Lecture 11: Tensor products and algebras ( PDF )

Lecture 12: Free unstable algebras ( PDF )

Lecture 13: The dual Steenrod algebra ( PDF )

Lecture 14: The Frobenius ( PDF )

Lecture 15: Finiteness conditions ( PDF )

Lecture 16: Some unstable injectives ( PDF )

Lecture 17: Injectivity of tensor products ( PDF )

Lecture 18: Lannes’ T-functor ( PDF )

Lecture 19: Properties of T ( PDF )

Lecture 20: The T-functor and unstable algebras ( PDF )

Lecture 21: Free E-infinity algebras ( PDF )

Lecture 22: A pushout square ( PDF )

Lecture 23: The Eilenberg-Moore spectral sequence ( PDF )

Lecture 24: Operations on E-infinity algebras ( PDF )

Lecture 25: T and the cohomology of spaces ( PDF )

Lecture 26: Profinite spaces ( PDF )

Lecture 27: p -adic homotopy theory ( PDF )

Lecture 28: Atomicity ( PDF )

Lecture 29: Atomicity of connected p-Finite spaces ( PDF )

Lecture 30: The Sullivan conjecture ( PDF )

Lecture 31: p-Profinite completion of spaces ( PDF )

Lecture 32: The arithmetic square ( PDF )

Lecture 33: The Sullivan conjecture revisited ( PDF )

Lecture 34: Quaternionic projective space ( PDF )

Lecture 35: Analytic functors revisited ( PDF )

Lecture 36: The Nil-filtration ( PDF )

Lecture 37: The Krull filtration ( PDF )

Lecture 38: Epilogue ( PDF )