# Fall 2015 MATH 215A 001 LEC

Section | Days/Time | Location | Instructor | CCN |
---|---|---|---|---|

001 LEC | MWF 11-12P | 740 EVANS | HARRISON, V C | 54464 |

Units/Credit | Final Exam Group | Enrollment |
---|---|---|

4 | 2: MONDAY, DECEMBER 14, 2015 1130-230P | Limit:25 Enrolled:15 Waitlist:0 Avail Seats:10 [on 10/04/15] |

**Prerequisites:** 113, 110 and point-set topology (e.g. 202A).

**Syllabus:** Fundamental group and covering spaces, simplicial and singular homology theory with applications, cohomology theory, duality theorem. Homotopy theory, fibrations, relations between homotopy and homology, obstruction theory, and topics from spectral sequences, cohomology operations, and characteristic classes. Sequence begins fall.

**Office:** Professor Jenny Harrison, 829 Evans Hall

**Office Hours:** MWF, 1-2 pm

**Required Text: **

- M J Greenberg and J Harper, Algebraic Topology: a First Course (Benjamin/Cummings 1981)
- A Hatcher, Algebraic Topology (Cambridge University Press, paperback, 2002)
- G E Bredon, Topology and Geometry (Springer GTM 139, 1993)

Hatcher is excellent and available as a free pdf, as is Greenberg & Harper. The latter went out of print some years ago, but it uses a more categorical and concise approach than Hatcher. Bredon provides useful material on differentiable manifolds which will give us concrete examples to work with.

**Recommended Reading:** Steve Awodey: Category Theory, Oxford University Press, 2010. This is a simpler version of the classic book by Eilenberg and Mac Lane. We will only be using some simple concepts from category theory, so this is optional reading.

**Grading:** Homework will be graded, hopefully, but the scores will not count towards your course grade.

**Homework:** There will be weekly homework assignments and a final exam which will be based 75% on homework and 25% on material from the lectures.

**Course Webpage:** https://bcourses.berkeley.edu/courses/1325765