MTH 532/632: Topology II (Differential Topology)
University of Miami, Spring 2022
Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: TBD (or by appointment)
Each office hour session is currently on Zoom.
Class Time and Location: MWF 9:15-10:05 in Ungar 411.
Course syllabus can be found here.
Text: Differential Topology by Guillemin and Pollack
Homework Assignments
| Assignment |
Due Date |
| Homework 1: Ch 1 § 1: # 2, 3, 12; Ch 1 § 2: # 2, 4, 8; Ch 1 § 4: #1 |
2/2/22 |
| Homework 2: Ch 1 § 3: # 1, 2; Ch 1 § 4: 1, 2, 7; Ch 1 § 7: 1, 4 |
2/14/22 |
| Homework 3: Ch 1 § 5: 2, 4, 7; Ch 1 § 6: 7; Ch 2 § 1: 4, 5 |
2/28/22 |
| Homework 4: Ch 2 § 3: # 4; Ch 2 § 4: # 4, 5, 6, 7, 8, 11 |
3/21/22 |
Course Schedule
| Date |
Lecture Content |
Reading |
Notes |
| 1/19/22 |
Introduction to the course. Syllabus. |
Ch 1 § 1 |
lec01 |
| 1/21/22 |
Examples of manifolds. |
Ch 1 § 1 |
lec02 |
| 1/24/22 |
Derivatives and tangents. Statement of Rank Theorem. |
Ch 1 § 2, 3 |
lec03 |
| 1/26/22 |
Proof of Rank Theorem and some corollaries. |
Ch 1 § 3, 4 |
lec04 |
| 1/31/22 |
Examples of derivatives. Preimage Theorem. |
Ch 1 § 4 |
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| 2/2/22 |
Preimage Theorem: examples. |
Ch 1 § 4 |
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| 2/7/22 |
Submanifolds and embeddings. |
Ch 1 § 3 |
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| 2/9/22 |
Sard's Theorem. |
Ch 1 § 7 |
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| 2/14/22 |
Applications of Sard's Theorem. |
Ch 2 § 1, 2 |
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| 2/16/22 |
Transversality. |
Ch 1 § 5 |
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| 2/21/22 |
Transversality Theorem: explanation and implications. |
Ch 2 § 3 |
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| 2/23/22 |
Transversality Theorem: proof. Epsilon-neighborhood Theorem. |
Ch 2 § 3 |
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| 2/28/22 |
Intersection Theory mod 2. |
Ch 2 § 4 |
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| 3/2/22 |
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| 3/7/22 |
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| 3/9/22 |
Midterm |
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| 3/14/22 |
Spring break |
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| 3/16/22 |
Spring break |
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| 3/21/22 |
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| 3/23/22 |
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| 3/28/22 |
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| 3/30/22 |
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| 4/4/22 |
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| 4/6/22 |
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| 4/11/22 |
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| 4/13/22 |
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| 4/18/22 |
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| 4/20/22 |
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| 4/25/22 |
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| 4/27/22 |
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| 5/2/22 |
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