Course: | MATH 7512 Topology II |
Time and Place: | Tuesday & Thursday, 9:10 - 10:30 AM, in 282 Lockett |
Instructor: | Dan Cohen |
Office Hours: |
Tuesday & Thursday, 10:30 - 11:30 AM in 372 Lockett,
and by appointment. G. Pruidze, the teaching assistant for this course, will also hold an office hour Monday, 2:30 - 3:30 PM in 379 Lockett. |
Prerequisites: | MATH 7510 Topology I, and basic group theory. |
Grade: |
Based on homework (~80%) and a final exam (~20%).
Homework will be announced in class,
and posted
here.
The final will probably be an in-class exam. |
Text: |
Topology, by J. Munkres (second edition).
We will cover portions of Part II, Chapters 9 - 14.
Other sources for material covered in this course include: Algebraic Topology, by A. Hatcher, Chapters 0 & 1. A Basic Course in Algebraic Topology, by W. Massey, Chapters I - V. |
The focus of MATH 7512 is on one such algebraic invariant, the fundamental group (consisting, loosely speaking, of unshrinkable loops in the topological space in question). Using this tool, we can (attempt to) reduce topological problems about spaces to purely algebraic problems about groups. For instance, with the fundamental group, we will be able to distinguish between the surface of a donut and the surface of a sphere, despite the fact that these surfaces appear the same on a small scale.
We will also pursue a number of topics and applications related to the fundamental group, including covering space theory, the Ham Sandwich Theorem, and even the Fundamental Theorem of Algebra. Time permitting, we may also pursue topics such as Kurosh's theorem on subgroups of free groups, methods for describing the fundamental group of the complement of a knot, and braids.
Department of Mathematics
MATH 7512 homepage: | http://www.math.lsu.edu/~cohen/courses/SPRING05/M7512.html |
MATH 7512 homework: | http://www.math.lsu.edu/~cohen/courses/SPRING05/M7512hw.html |