MATH-GA.2310-001 Topology I
After introducing metric spaces and topological spaces, the emphasis will be on the algebraic topology of manifolds and cell complexes. Elements of algebraic topology to be covered include fundamental groups and covering spaces, and homotopy. Additional material may be covered at the discretion of the instructor, such as degree theory, transversality and intersection theory, and examples from knot theory.
Any knowledge of groups, rings, vector spaces and multivariable calculus is helpful. Undergraduate students planning to take this course must have V63.0343 Algebra I or permission of the Department.
- Hatcher, A. (2002). Algebraic Topology. New York, NY: Cambridge University Press
- Munkres, J. (2000). Topology (2nd ed.). Upper Saddle River, NJ: Prentice-Hall/ Pearson Education
- Guillemin, V., Pollack, A. (1974). Differential Topology. Englewood Cliffs, NJ: Prentice-Hall
- Milnor, J.W. (1997). Princeton Landmarks in Mathematics [Series]. Topology from a Differentiable Viewpoint (Rev. ed.). Princeton, NJ: Princeton University Press