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Course, academic year 2023/2024
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Introduction to Differential Topology - NMAG452
Title: Úvod do diferenciální topologie
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Petr Somberg, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Topology and Category
Incompatibility : NMAT009
Interchangeability : NMAT009
Annotation -
Last update: T_MUUK (02.03.2017)
Differential topology studies the relationship between analytic concepts (critical points of functions or functionals, solution spaces of systems of PDEs, zeroes of vector fields, diffeomorphism groups, etc) and topological concepts (Euler characteristics, CW structure, homotopy type, intersection forms, etc). We will focus on basic aspects of Sard's Theorem and Morse theory and their applications.
Course completion requirements -
Last update: Roman Golovko, Ph.D. (30.04.2020)

There will be several homeworks. As a requirement to take the final exam students must submit

solutions to at least one homework. The final exam will be in the form of a distance interview.

Literature -
Last update: doc. RNDr. Petr Somberg, Ph.D. (02.03.2017)

Lee, J. : Introduction to Smooth Manifolds, Springer 2012

Hirsch, M. W. : Differential Topology, Springer 1997

Kock, J. : Frobenius Algebras and 2D Topological Quantum Field Theories, Cambridge 2003

Requirements to the exam
Last update: Roman Golovko, Ph.D. (18.02.2019)

For the oral part of the exam it is necessary to know the whole content of lecture.

You will get time to write a preparation for the oral part which the knowledge of definitions, theorems and their proofs is tested.

We test as well the understanding to the lecture, you will have to prove an easy theorem which follows from statements from the lecture.

Syllabus -
Last update: Roman Golovko, Ph.D. (18.02.2019)

(Nondegenerate) critical point, critical value and regular value of a smooth map,

Sard's theorem, Morse theory and CW decomposition.

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