MTH 532/632: Differential Topology
University of Miami, Spring 2026
Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: 10am-11am Tuesday, 8am-9am Thursday, or by appointment
Time and Location: TuTh 11am-12:15pm, Dooly Memorial 209
Course syllabus can be found here.
Text: Differential Topology by Guillemin and Pollack
The symbol § used below means "Section".
Homework Assignments
All homeworks are worth the same, even if graded out of different totals.
| Assignment |
Due Date |
Remarks |
| Homework 1: Ch 1 § 1: # 2, 3, 7, 9, 12; Ch 1 § 2: # 2, 4, 8 |
1/22/26 |
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| Homework 2: Ch 1 § 3: # 1, 2; Ch 1 § 4: # 1, 2, 5, 6, 7 |
2/3/26 |
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| Homework 3: Ch 1 § 4: # 11, 12; Ch 1 § 7: # 1, 3, 4, 7 |
2/12/26 |
|
Course Schedule
| Date |
Lecture Content |
Reading |
| 1/13/26 |
Syllabus overview, introduction, definition of smooth manifold, examples |
§ 1.1 |
| 1/15/26 |
Survey on classification of manifolds, derivatives and tangent spaces |
§ 1.2 |
| 1/20/26 |
Class cancelled by Provost |
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| 1/22/26 |
More derivatives. Examples: sphere, Hopf map. |
§ 1.3, 1.4, video |
| 1/27/26 |
Local structure of smooth maps. Rank Theorem. |
§ 1.3, 1.4 |
| 1/29/26 |
Critical/regular values. Preimage Theorem. |
§ 1.4 |
| 2/3/26 |
Preimage Theorem: examples. Matrix groups as manifolds. |
§ 1.4, img1, img2 |
| 2/5/26 |
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| 2/10/26 |
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| 2/12/26 |
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| 2/17/26 |
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| 2/19/26 |
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| 2/24/26 |
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| 2/26/26 |
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| 3/3/26 |
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| 3/5/26 |
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| 3/10/26 |
Spring break |
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| 3/12/26 |
Spring break |
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| 3/17/26 |
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| 3/19/26 |
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| 3/24/26 |
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| 3/26/26 |
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| 3/31/26 |
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| 4/2/26 |
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| 4/7/26 |
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| 4/9/26 |
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| 4/14/26 |
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| 4/16/26 |
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| 4/21/26 |
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| 4/23/26 |
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