Geometry
 & Topology
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Graduate Course

Lecturers:
Eaman Eftekhary & Meysam Nassiri
(School of Mathematics, IPM)

Title:
Topology of Smooth Manifolds

Date: Thursdays, Fall 2018

Time: 8:30-10:00 & 10:30-12:00

(First lecture: Thursday, September 27, 2018, 8:30 a.m.)

Location: Lecture Hall 2,
Niavaran Building, IPM
Sh. Bahonar (Niavaran) Square, Tehran

Description:
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.
- 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.

Problem Sets:





School of Mathematics,
IPM - Institute for Research in Fundamental Sciences
Niavaran Building, Niavaran Square, Tehran, Iran
Tel: +98 21 222 90 928
Email: gt@ipm.ir