Instructor: Marco Gualtieri [
] office 2-244
Prerequisite: Introduction to Topology 18.901
Primary textbook: W.S. Massey, Algebraic Topology: An Introduction. Graduate Texts in Mathematics 56, Springer-Verlag, 1977. (BEWARE! GTM 70 and GTM 127 are also by Massey. Do not be led astray.)
Secondary textbook: A. Hatcher, Algebraic Topology. Cambridge University Press, 2002. Availbale (free) online here.
Course description: This course is an introduction to algebraic topology, a field in which the shape of topological spaces is studied using tools from algebra, such as groups and rings. Is the 2-dimensional sphere homeomorphic to a torus? What are all possible 2-dimensional spaces? Is the Euclidean plane homeomorphic to Euclidean 3-d space? We can comb the hair on a circle flat, but what about on a 2-sphere? Is it possible on a 3-sphere? These are some of the questions we will answer in this class.
The class is a seminar course, meaning the students present the lectures: there will be two lectures of 30-40 minutes in each meeting, with discussion encouraged. For your first lectures of the term, make an appointment with me to practise your lecture.
There is also a written report of approximately 10 LaTeX pages (don't worry, TeX is facile), on a topic in algebraic toplology which you find interesting and which we won't cover in the seminar (until you present the report at the end). I will suggest a list of possible projects, and you may suggest any topics which interest you. In any case you should discuss your choice with me. Deadline for choosing topic (email or tell me in person): March 8. Deadline for first draft (submit by email, including .tex and .PDF file): April 13. I will make corrections/comments. Deadline for final draft, incorporating corrections/comments (submit by email, include .tex and .PDF file): Monday, April 30.
Final grade: 70% lectures/class participation (quality and improvement of lectures, attendance), 30% written report. No homework or exams.