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Sullivan’s Conjecture is prompted by Homotopy Theory concerning the fixed point set in group actions of a finite group. The main purpose of this [course_title] is to facilitate your understanding of Sullivan’s Conjecture easily but effectively. That’s why this [course_title] describes some of the tools used to enter into the proof of Sullivan’s Conjecture.


This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer need to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.


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Course Credit: MIT

Course Curriculum

Module: 01
Introduction 00:30:00
Steenrod operations 00:30:00
Basic properties of Steenrod operations 00:45:00
The Adem relations 00:30:00
The Adem relations (cont.) 00:45:00
Admissible monomials 00:30:00
Module: 02
Free unstable modules 00:45:00
A theorem of Gabriel-Kuhn-Popesco 00:30:00
Injectivity of the cohomology of BV 00:30:00
Generating analytic functors 00:45:00
Tensor products and algebras 00:30:00
Free unstable algebras 00:30:00
Module: 03
The dual Steenrod algebra 00:30:00
The Frobenius 00:45:00
Finiteness conditions 00:45:00
Injectivity of tensor products 00:45:00
Lannes’ T-functor 00:30:00
Properties of T 00:30:00
The T-functor and unstable algebras 00:45:00
Module: 04
Free E-infinity algebras 00:30:00
A pushout square 00:30:00
The Eilenberg-Moore spectral sequence 00:45:00
Operations on E-infinity algebras 00:30:00
T and the cohomology of spaces 00:30:00
Profinite spaces 00:30:00
Module: 05
p-adic homotopy theory 00:45:00
Atomicity 00:45:00
Atomicity of connected p-Finite spaces 00:45:00
The Sullivan conjecture 00:45:00
p-Profinite completion of spaces 00:30:00
The arithmetic square 00:45:00
Module: 06
The Sullivan conjecture revisited 00:45:00
Quaternionic projective space 00:45:00
Analytic functors revisited 00:30:00
The Nil-filtration 00:30:00
The Krull filtration 00:45:00
Epilogue 00:30:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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