Math 2320: Topology II

Course Information

Syllabus

Official description in the NYU Catalog

Class meets: T 7:10-9pm at WWH 517.

Instructor: Benjamin Bakker

email: (last name)-at-cims-dot-nyu-dot-edu

Office Hours: M 4-5pm in Warren Weaver Hall 619

Homework

• • Homework 1.

  • Homework 2.

  • Homework 3.

  • Homework 4.

  • Homework 5.

  • Homework 6.

  • Homework 7.

  • Homework 8.

  • Homework 9.

  • Oral exam questions.

Lecture Topics and References

Lecture 1: Review of covering space theory and the fundamental group. Lecture Notes.

Lecture 2: Existence of the universal cover. Simplicial homology. Lecture Notes.

Lecture 3: Some computations in simplicial homology. Lecture Notes.

Lecture 4: Singular homology. Lecture Notes.

Lecture 5: Classical applications. Equivalence of singular and simplicial homology. Lecture Notes.

Lecture 6: Excision. Lecture Notes.

Lecture 7: CW homology. Lecture Notes.

Lecture 8: Cohomology. Lecture Notes.

Lecture 9: Cup product. Lecture Notes.

Lecture 10: Topology of manifolds. Lecture Notes.

Lecture 11: Poincare duality i. Lecture Notes.

Lecture 12: Poincare duality ii. Lecture Notes.

Lecture 13: Homotopy groups. Lecture Notes.

Lecture 14: Introduction to differential topology. Lecture Notes.