MTH 532/632: Topology II (Differential Topology)
University of Miami, Spring 2025
Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: 10-11 Tuesday, or by appointment
Class Time and Location: 11:00-12:15 Tuesdays and Thursdays in Dooly Memorial 112.
Course syllabus can be found here.
Text: Differential Topology by Guillemin and Pollack
The symbol § used below means "Section".
Homework Assignments
| Assignment |
Due Date |
| Homework 1: Ch 1 § 1: # 2, 3, 7, 9, 12; Ch 1 § 2: # 2, 4, 8
| 1/23/23 |
| Homework 2: Ch 1 § 3: # 1, 2; Ch 1 § 4: 1, 2, 5, 6, 7
| 2/4/23 |
Course Schedule
| Date |
Lecture Content |
Reading |
Notes |
| 1/14/23 |
Introduction. Smooth functions. Definition of manifolds, examples. |
§ 1.1 |
|
| 1/16/23 |
More examples of manifolds. Tangent spaces and derivatives. |
§ 1.1, 1.2 |
|
| 1/21/23 |
More on derivatives. Chain rule. Example: spheres. |
§ 1.2 |
|
| 1/23/23 |
Detailed examples: Hopf map, 2-torus. |
§ 1.3, 1.4 |
|
| 1/28/23 |
Local structure of smooth maps. Rank Theorem. |
§ 1.3, 1.4 |
|
| 1/30/23 |
Critical/regular values. Preimage Theorem. |
§ 1.4 |
|
| 2/4/23 |
Applications of Preimage Theorem. |
§ 1.4 |
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| 2/6/23 |
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| 2/11/23 |
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| 2/13/23 |
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| 2/18/23 |
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| 2/20/23 |
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| 2/25/23 |
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| 2/27/23 |
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| 3/4/23 |
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| 3/6/23 |
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| 3/11/23 |
Spring break |
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| 3/13/23 |
Spring break |
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| 3/18/23 |
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| 3/20/23 |
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| 3/25/23 |
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| 3/27/23 |
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| 4/1/23 |
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| 4/3/23 |
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| 4/8/23 |
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| 4/10/23 |
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| 4/15/23 |
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| 4/17/23 |
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| 4/22/23 |
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| 4/24/23 |
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