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The goal of this course is to describe some of the tools which enter into the proof of Sullivan’s conjecture.

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Massachusetts Institute of Technology

November 7, 2022

UK

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November 7, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

The goal of this course is to describe some of the tools which enter into the proof of Sullivan’s conjecture.

Course Curriculum

  • Introduction Unlimited
  • Steenrod operations Unlimited
  • Basic properties of Steenrod operations Unlimited
  • The Adem relations Unlimited
  • The Adem relations (cont.) Unlimited
  • Admissible monomials Unlimited
  • Free unstable modules Unlimited
  • A theorem of Gabriel-Kuhn-Popesco Unlimited
  • Injectivity of the cohomology of BV Unlimited
  • Generating analytic functors Unlimited
  • Tensor products and algebras Unlimited
  • Free unstable algebras Unlimited
  • The dual Steenrod algebra Unlimited
  • The Frobenius Unlimited
  • Finiteness conditions Unlimited
  • Some unstable injectives Unlimited
  • Injectivity of tensor products Unlimited
  • Lannes’ T-functor Unlimited
  • Properties of T Unlimited
  • The T-functor and unstable algebras Unlimited
  • Free E-infinity algebras Unlimited
  • A pushout square Unlimited
  • The Eilenberg-Moore spectral sequence Unlimited
  • Operations on E-infinity algebras Unlimited
  • T and the cohomology of spaces Unlimited
  • Profinite spaces Unlimited
  • p-adic homotopy theory Unlimited
  • Atomicity Unlimited
  • Atomicity of connected p-Finite spaces Unlimited
  • The Sullivan conjecture Unlimited
  • p-Profinite completion of spaces Unlimited
  • The arithmetic square Unlimited
  • The Sullivan conjecture revisited Unlimited
  • Quaternionic projective space Unlimited
  • Analytic functors revisited Unlimited
  • The Nil-filtration Unlimited
  • The Krull filtration Unlimited
  • Epilogue Unlimited

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Massachusetts Institute of Technology