
Math 869: Algebraic TopologySpring Semester 2007
Background and goals: This course is the Topology part of the qualifying sequence of Math 868869: Geometry/Topology. The fundamental question that we seek to answer in this course is: how can we tell whether two manifolds are homeomorphic? Over the course of the 20th century, mathematicians have developed a number of algebraic tools to help answer this question. The tools that we will study are the fundamental group (including covering spaces and van Kampen's theorem), homology theory, and some cohomology theory.
Textbook: Agebraic Topology, by Allen Hatcher. We will cover most of Chapters 1 and 2, plus part of Chapter 3. Prerequisites: a good grounding in undergraduate algebra, plus some background in topological spaces. For example, MTH 310, MTH 411, and MTH 461 would do the trick. This course is almost entirely independent of MTH 868. Grading: The final grade is based on homework (60%) and a takehome final (40%). Homework will be due weekly, typically on Wednesdays. No late homework is acceptable; however, I will drop your lowest homework grade. Discussion sections: We will have one weekly discussion section, led by Inanc Baykur. This will focus on examples related to the lectures; sometimes, we'll also go over homework problems. Participation in this seminar is mandatory.
Homework assignments
dfuter at temple edu Last modified: Wed Aug 23 13:41:22 PDT 2006 