SS 01 - Introduction and Motivation
https://youtube.com/playlist?list=PLwKdCQGFDsilSxtnDfgP4tJ8SE1So1ecS&si=SfhLIw6CMQiObiJH
Spectral Sequences - Spring 2020 at UCLA
Motivation and Setup: SS01-SS11
Bockstein Spectral Sequence: SS12-SS14
Serre Spectral Sequence: SS15-SS28
Stable Homotopy Groups: CSS29, SS47-SS49
Double Complexes: SS30-SS37
Convergence: SS38-SS46
Resources
Extra chapter on spectral sequences - Hatcher
Spectral sequences: friend or foe? - Vakil
Lecture notes in algebraic topology - Davis and Kirk
Cohomology operations and applications in homotopy theory - Mosher and Tangora
A user's guide to spectral sequences - McCleary
A user's guide to the Bockstein spectral sequence - Palmieri
Spectral sequences and an application - Orlich
Conditionally convergent spectral sequences - Boardman
An introduction to homological algebra - Weibel
Suggested Presentation Topics
Bockstein spectral sequence and H-spaces
Proof of cohomological Serre spectral sequence with algebra structure
Higher structure in Serre spectral sequence (e.g. coalgebras and/or Hopf algebras)
Proof of existence of Steenrod squares and properties
Computation of K(Z/2,n) with integral coefficients using Bockstein spectral sequence
Odd prime Steenrod operations
Proof of Thom isomorphism using Serre spectral sequence
Computations in and/or construction of:
The Serre spectral sequence with local coefficients
The Bökstedt spectral sequence
The Atiyah-Hirzebruch spectral sequence
The Künneth spectral sequence
The change-of-rings spectral sequence
The Cartan-Leray spectral sequence
The slice spectral sequence
The Bousfield-Kan spectral sequence
The homotopy fixed-point spectral sequence
少年，你想不想加速到更快的世界？
谱序列
（1/49）
2374播放
简介
订阅合集
SS 01 - Introduction and Motivation
09:38
SS 02 - Graded Rings and Modules
16:43
SS 03 - Spectral Sequence Definition
13:44
SS 04 - First Quadrant Spectral Sequence
15:13
SS 05 - Homology 1st Quadrant Spectral Sequence
09:21
SS 06 - Unraveled Exact Couple (Part 1)
10:12
SS 07 - Unraveled Exact Couple (Part 2)
23:07
SS 08 - Unraveled Exact Couple (Part 3)
08:21
SS 09 - Cohomology Spectral Sequence for a Filtration
18:33
SS 10 - Unraveled Exact Couple (Part 4)
13:17
SS 11 - Exact Couple
18:24
SS 12 - Bockstein Spectral Sequence
20:49
SS 13 - Bockstein Spectral Sequence 1st Application
23:12
SS 14 - Bockstein SS from a Filtration
13:36
SS 15 - Serre Spectral Sequence
14:34
SS 16 - Serre Spectral Sequence Sketch
09:52
SS 17 - Loop-path Fibration
10:34
SS 18 - First Computations (Part 1)
19:27
SS 19 - First Computations (Part 2)
27:29
SS 20 - An Application of the Serre Spectral Sequence
10:30
SS 21 - The Steenrod Squares
14:58
SS 22 - The Steenrod Algebra
18:46
SS 23 - Unstable modules over A
24:08
SS 24 - Cohomology of Eilenberg-MacLane Spaces (Part 1)
20:37
SS 25 - Cohomology of Eilenberg-MacLane Spaces (Part 2)
25:04
SS 26 - Cohomology of Eilenberg-MacLane Spaces (Part 3)
29:07
SS 27 - Cohomology of Eilenberg-MacLane Spaces (Part 4)
20:43
SS 28 - Cohomology of Eilenberg-MacLane Spaces (Part 5)
24:16
SS 29 - Calculating First Stable Stem
29:41
SS 30 - Double Complex
12:24
SS 31 - Double Complex Spectral Sequence
18:51
SS 32 - Some Applications (Part 1)
12:24
SS 33 - Some Applications (Part 2)
23:16
SS 34 - Grothendieck Spectral Sequence
16:28
SS 35 - Base Change
15:06
SS 36 - Construction of Grothendieck Spectral Sequence (Part 1)
15:15
SS 37 - Construction of Grothendieck Spectral Sequence (Part 2)
23:45
SS 38 - Cohomology Spectral Sequence for a Filtration (Part 1)
23:20
SS 39 - Cohomology Spectral Sequence for a Filtration (Part 2)
22:47
SS 40 - Convergence (Part 1)
37:41
SS 41 - Convergence (Part 2)
32:00
SS 42 - Convergence (Part 3)
32:33
SS 43 - Convergence (Part 4)
39:26
SS 44 - Convergence (Part 5)
26:34
SS 45 - Convergence (Part 6)
34:52
SS 46 - Convergence Examples
27:37
SS 47 - Stable Stems are Finite
30:03
SS 48 - Computing More Stable Stems (Part 1)
27:26
SS 49 - Computing More Stable Stems (Part 2)
47:25
顶部