Differential Topology (ΓΕ4)
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | ΓΕ4 |
Semester | 2 |
Course Title | Differential Topology |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
Course Type | Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students | Yes (in Greek) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
In this lecture we present applications of Algebraic and Differential Topology in the study of topological invariants of smooth manifolds. |
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General Competences |
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Syllabus
- Manifolds.
- Immersions, embeddings and submersions.
- Milnor’s proof of the fundamental theorem of algebra.
- Sard’s theorem and Morse functions.
- Partition of unity and Whitney’s embedding theorem.
- Homotopy and isotopy.
- Brouwer’s degree.
- Whitney’s approximation theorem.
- Differential forms and integration.
- Hopf's invariant.
- Hopf's degree theorem.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
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Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
Weakly HomeWorks, presentations in the blackboard of HomeWorks, written final examination. |
Attached Bibliography
- T. Bröcker, K. Jänich, Introduction to differential topology, Cambridge Univ. Press, 1982.
- V. Guillemin and A. Pollack, Differential Topology, Prentice Hall, 1974.
- J. Milnor, Morse Theory, Annals of Mathematical Studies, 51. Princeton University Press, Princeton, N.J. 1963.
- J. Milnor, Topology from a differentiable viewpoint, The University Press of Virginia, Charlottesville, Va. 1965.