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.
Last update: T_MUUK (02.03.2017)
Differenciální topologie zkoumá vztah mezi analytickými pojmy (kritické body funkcí a funkcionálů, prostory řešení
systémů PDR, nuly vektorových polí, grupy difeomorfismů apod.) a topologickými pojmy (Eulerova charakteristika,
CW struktura, homotopický typ, interseční formy apod.) Budeme se věnovat základním aspektům Sardovy věty a
Morseovy teorie a jejich aplikacím.
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.
Last update: Roman Golovko, Ph.D. (30.04.2020)
Bude zadáno několik domácích úkolů. Podmínkou k zápočtu je odevzdání alespoň jednoho správného řešení.
Zkouška má formou distančního pohovoru.
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
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.
Last update: Mgr. Dalibor Šmíd, Ph.D. (11.06.2021)
(Nedegenerovaný) kritický bod, kritická hodnota a regulární hodnota hladkého zobrazení, Sardova věta, Morseova teorie a CW rozklad.
