MATH5070 - Topology of Manifolds - 2022/23

Announcement

• Syllabus [Download file]
• Topic of Final Projects [Download file]

General Information

Lecturer

• Prof. Zhongtao WU
  • Office: LSB 216
  • Tel: 3943-8578
  • Email:

Time and Venue

• Lecture: Th 2:30PM - 5:15PM, Lady Shaw Bldg 222

Course Description

This course is an introduction to several basic topological invariants for manifolds. Major topics are: differentiable manifolds and maps, Sard's Theorem, degree of maps, fundamental group, covering space, homology group. Students taking this course are expected to have knowledge in elementary analysis.

References

• Frank Warner, Foundations of Differentiable Manifolds and Lie Groups
• John Milnor, Topology from the Differentiable Viewpoint
• Ib Madsen and Jorgen Tornehave, From Calculus to Cohomology

Assignments

• HW1, due Sep. 21
• HW2, due Oct. 5
• HW3, due Oct. 19
• HW4, due Nov. 2
• HW5, due Nov. 16
• HW6, due Dec. 14
• Final Project, due Dec. 21

Solutions

• Solution 1
• Solution 2
• Solution 3
• Solution 4

Assessment Scheme