2018/2019
Научно-исследовательский семинар "Геометрия и топология"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Преподаватели:
Горбунов Василий Геннадьевич
Язык:
английский
Кредиты:
5
Контактные часы:
76
Course Syllabus
Abstract
The course covers basic notions of topology such as metric spaces, smooth manifolds and fundamental group. The main focus is on concrete examples such as Riemann surfaces, projective spaces, Grassmannians. The course can serve as an introduction to more advanced geometry and topology courses.
Learning Objectives
- The seminar is intended to give a background on contemporary geometry and topology.
Expected Learning Outcomes
- Successful participants will be able to rigorously justify geometric heuristics, to apply methods of topology to various problems in mathematics.
Course Contents
- Reminder on set theory: countable and uncountable sets, Cantor set, axiom of choice, non-measurable set.
- Point-set topology: topological spaces, open and closed subsets, continuous functions, homeomorphism and homotopy equivalence.
- Metric spaces, compactness, manifolds. Peano curve and Cantor staircase function.
- Fundamental group and covering spaces, Riemann surfaces.
- Projective spaces and Grassmannians.
Assessment Elements
- Cumulative gradecumulative grade is proportional to number of tasks solved.
- Final exam
Bibliography
Recommended Core Bibliography
- Ash, R. B. (2009). Real Variables with Basic Metric Space Topology (Vol. Dover edition). Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1150123
Recommended Additional Bibliography
- Allen Hatcher. (2002). Algebraic topology. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.87FE219C