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.
Assessment
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.
Certification
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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 | ||
Assessment | |||
Submit Your Assignment | 00:00:00 | ||
Certification | 00:00:00 |
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