## Math 225C: Algebraic Topology

### Spring 2017

**Instructor:** Sucharit Sarkar.

**Class:** MWF 1-1:50pm, MS 7608.

**Office hours:** Th 2-2:50pm and F 10-11:50am, MS 6909.

**TA:** Kevin Carlson.

**TA discussion section:** Th 1-1:50pm, MS 7608.

**TA office hours:** By appointment.

**Textbook:** Hatcher,

Algebraic Topology, Chapters 1-3.

**Syllabus:** Basic concepts of homotopy theory, fundamental group,
Van Kampen theorem, and covering spaces, singular homology and
cohomology theory, axioms of homology theory, Mayer-Vietoris sequence,
excision, cup products, calculation of homology and cohomology of
standard spaces, cell complexes and cellular homology, Poincare
duality.

**Prerequisites:** Basic knowledge of algebra and point set
topology. Try these

problems to
check your preparedness.

**Useful
links:** Department
page,

University
page,

MyUCLA gradebook.

**Homework:** Homeworks are due at the beginning of lecture on
Monday. Do not submit homework by e-mail. No late homework will be
accepted.

HW |
Due on |
Problems |

1 |
4/10 |
**0:** 1, 2, 3, 13, **1.1:** 1, 2, 3, 5, 6. |

2 |
4/17 |
**0:** 14, 15, 16, **1.1:** 8, 9, 16, **1.2:** 3, 6, 7, 8. |

3 |
4/24 |
**1.3:** 4, 6, 9, 10, 12, 13, 19, 27, 32. |

4 |
5/1 |
**2.1:** 1, 2, 3, 4, 5, 6, 7, 8, 9. |

5 |
5/8 |
**2.1:** 10, 11, 12, 13, 14, 15, 16, 18, 30. |

6 |
5/15 |
**2.1:** 17, 20, 21, 22, 29, 31, **2.2:** 27, 28, 29. |

7 |
5/22 |
**2.2:** 2, 3, 4, 5, 7, 8, 9, 10, 12. |

8 |
5/31 |
**2.2:** 14, 15, 17, 19, 20, 21, 22, 23, 33, 43. |

9 |
6/5 |
**2.2:** 40, 41, **3.1:** 5, 6, 8, 9, **3.A:** 1, 3, **3.B:** 1, 2. |

10 |
6/12 |
**3.2:** 1, 3, 5, 7, 8, 11, 12. |

You are encouraged to work in groups on your homework; this is
generally beneficial to your understanding and helps you learn how to
communicate clearly about mathematics. However, you must write up all
solutions yourself. Moreover, since crediting your collaborators is an
important element of academic ethics, you should write down with whom
you worked at the top of each assignment. You should also cite any
sources (other than lectures and the textbook) that you use.

**Exams:** 225C-finals.pdf (Link
active 6/9-6/16)

The final take-home final exam due on 6/16. Once again, you are free
to collaborate and consult textbooks and notes, but you must write up
all the solutions yourself, and you must credit your sources and
collaborators. Submitting the final exam is mandatory. In particular,
note that university policy requires that a student who misses the
finals be automatically given F, unless it is due to extreme and
documented circumstances, in which case, if the performance in the
course is otherwise satisfactory, the grade might be I.

**Grading: ** Numerical grades will be recorded in the MyUCLA
gradebook. The composite numerical grade will be computed as 70% HW +
30% Final, and the final letter grades will be assigned based on that.
If you believe a problem on a homework or an exam has been graded
incorrectly, or that your score was not correctly recorded in the
MyUCLA gradebook, you must bring this to the attention of the
instructor within 10 calendar days of the due date of the assignment
in question, or the date of the exam, and before the end of the
quarter (6/16). Grading complaints not initiated within this period of
time will not be considered. Please verify in a timely manner that
your scores are correctly recorded on MyUCLA.