## MAT 1300, Topology I, Fall 2019

#### Instructor

Prof. Kasra RafiOffice: BA 6188 (Bahen Centre)

Email: rafi@math.toronto.edu

#### Meetings

Tuesdays 11-1 pm in BA 6183.Thursdays 11 - 12 pm in BA 6183.

#### Office hours

Tuesdays and Thursdays 3-4 pmor by appointment.

#### Teaching Assistant

Jack DingE-mail: jding@math.toronto.edu

You can contact Jack to set an appointment if you need to discuss the assignments.

#### Textbook

*Differential Topology*, by Victor Guillemin and Alan Pollack (Main)

*Topology from the Differentiable Viewpoint*, by John Milnor (Sumplimentary).

*Introduction to Smooth Manifolds*, by J. M. Lee (Suplimentary).

#### Course description

This course is an introduction to Differential Topology. We study the class of smooth manifolds. We will cover the entirety of the main textbook.

#### Marking scheme

Your course grade is computed as follows:

- Assignments 24% (6% for each assignment)
- Midterm 30%
- Final exam 46%

#### Assignments:

There will be 4 assignments, one from each chapter of the text book. These will be collected and graded. You are encouraged to work with other students on the homework problems. But you have to write your own solutions. Assignments are marked for correctness, but also clarity. Keep your solutions concise, and make sure the structure of your argument is clear. I suggest that you type out your solutions in LaTeX.

- Due October 1
- Read Chapter I of the text book titled
*Manifolds and Smooth Maps*. - Watch Videos of 3 lectures by John Milnor (1965).
- § 1: 12, 17.
- § 2: 5, 11.
- § 3: 3, 4.
- § 4: 2, 8.
- § 5: 2, 5, 10.
- § 6: 4, 9.
- § 7: 8, 16.
- § 8: 15.

- Read Chapter I of the text book titled
- Due October 15
- Read Chapter II of the text book titled
*Transversality and Intersection*. - § 1: 7, 8.
- § 2: 3, 7.
- § 3: 4, 7, 12, 16.
- § 4: 6, 7, 10, 12, 19.
- § 6: 1, 3.

- Read Chapter II of the text book titled
- Due November 12
- Read Chapter III of the text book titled
*Oriented Intersection Theory*. - Chapter II, § 5: 4--12, you do not have to hand this in.
- Chapter II, § 6: 1, 3.
- Chapter III, § 2: 2, 11, 17, 24.
- Chapter III, § 3: 2, 9, 11, 17.
- Chapter III, § 4: 1, 8, 11.

- Read Chapter III of the text book titled
- Due December 10
- Read Chapter IV of the text book titled
*Integration on Manifolds*. - Chapter III, § 5: 5, 11, 12.
- Chapter III, § 6: 7--13, you do not have to hand this in.
- Chapter IV, § 2: 3, 6, 10.
- Chapter IV, § 4: 5, 8, 9, 12.
- Chapter IV, § 5: 2.
- Chapter IV, § 5: 2, 4, 8, 9, 11.

- Read Chapter IV of the text book titled

#### Midterm and Final Exams

The Midterm will take place on Tuesday October 15, during the class. Here is a copy of the Midterm.

The Final Exam will take place from 2 am - 5 pm on Tuesday December 10 in BA 6183.

#### Study hints

You should read the relevant sections of textbook, idealally before the lectures in class on the same meterial, and attempt most of the excersices in the textbook with your classmate. If the material is not clear you can try to find a different textbook on Differential Topology. Use the office hours and talk to the TA. The more time you spend with the material the more intuitive the concepts of the course will become.

#### Prerequisite

Linear Algebra; Vector Calculus; Point Set Topology.

Most of the background material can be found in
*Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus*
by Michael Spivak.

#### Academic integrity

The University of Toronto Code of Behaviour on Academic Matters can be found here.

#### Accessibility needs

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible: email disability.services@utoronto.ca or visit here.