This course is the first step
in a one-year program, aimed at introducing
topics in low dimensional topology and dynamical
systems to graduate students and
advanced undergraduates. The topics considered
for the first course include:

1- Smooth manifolds, Functions on
manifolds, Sard theorem

2- Intersection theory and Thom theorem

3- Vector fields, Lefschetz fixed-point
theorem

4- Differential forms, cohomology

5- Fundamental group, covering spaces and
lifting lemmas

6- Homology groups

7- Morse theory

**References:**

Guillemin and Pollack, Differential Topology. (**errata**)

Madsen and Tornehave, From Calculus to Cohomology.

Hatcher, Algebraic Topology.

The program continues with topic courses on low
dimensional topology and dynamical systems in
the second semester (and possibly summer).

** امکان ثبت نام
رسمی درس به عنوان دانشجوی مهمان در
پژوهشکده ریاضیاتِ پژوهشگاه دانشهای بنیادی
وجود دارد. **