Classifying spaces are objects of study in algebraic topology. In this course, we learn spectral sequences that are tools
in computation of the cohomology of classifying spaces.

The purpose of this course is to provide materials for writing a master's thesis in algebraic topology.

- Can explain classifying spaces.
- Can explain spectral sequences.
- Can compute cohomology using spectral sequences.

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1． | Classifying Space | Handouts | 200minutes |

2． | Spectral Sequence | Handouts | 200minutes |

3． | The Leray-Hirsh Theorem | Handouts | 200minutes |

4． | Gysin Sequence | Handouts | 200minutes |

5． | Eilenberg-MacLane Space | Handouts | 200minutes |

6． | The Transgression Theorem | Handouts | 200minutes |

7． | Review | Handouts | 200minutes |

8． | NA | NA | 0minutes |

9． | NA | NA | 0minutes |

10． | NA | NA | 0minutes |

11． | NA | NA | 0minutes |

12． | NA | NA | 0minutes |

13． | NA | NA | 0minutes |

14． | NA | NA | 0minutes |

Total. | - | - | 1400minutes |

Report | Total. | |
---|---|---|

1. | 10% | 10% |

2. | 20% | 20% |

3. | 70% | 70% |

Total. | 100% | - |

Report 100%. You will receive a passing grade if you understand the explanations given in the class and clearly state the
reasoning in your report.

Allen Hatcher, Algebraic topology, Cambridge University Press, 2002. http://pi.math.cornell.edu/~hatcher/AT/ATpage.html

Peter May, A Concise Course in Algebraic Topology, University of Chicago Press, 1999. http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf

Peter May, A Concise Course in Algebraic Topology, University of Chicago Press, 1999. http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf

Abstract algebra (group theory, linear algebra over finite fields), Point set topology, Category theory.

- Course that cultivates a basic self-management skills
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills

Work experience | Work experience and relevance to the course content if applicable |
---|---|

N/A | 該当しない |

- 4.QUALITY EDUCATION
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE

Last modified : Sun Mar 21 16:13:28 JST 2021