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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)
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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: Golovko Roman, Ph.D. (30.04.2020)
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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: Somberg Petr, doc. RNDr., Ph.D. (02.03.2017)
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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. Last update: Golovko Roman, Ph.D. (18.02.2019)
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(Nondegenerate) critical point, critical value and regular value of a smooth map, Sard's theorem, Morse theory and CW decomposition. Last update: Golovko Roman, Ph.D. (18.02.2019)
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