Details
Topology Notes
Euclidean and metric spaces
Topological spaces
Bases and manifolds
Subspaces
Products and disjoint unions
Quotients
Adjunction spaces and topological groups
Connectedness
Compactness
Cell and CW complexes
Compact surfaces
Homotopy and the fundamental group. I
The fundamental group. II
Homotopy equivalence
The circle
The fundamental group of the circle
Some applications of degree theory
Some group theory
Seifert–Van Kampen
Geometry Notes
Curves
Plane curves
Surfaces
Tangent planes
The first fundamental form
More on the first fundamental form
Area
Smooth maps
The derivative of a map
Conformal maps
Weingarten map and second fundamental form
Curvatures
Normal curvature
More on the curvatures
Theorema egregium
Theorema egregium II
Geodesics
Geodesics II
Gauss–Bonnet I
Gauss–Bonnet II
More on geodesics
Minimal surfaces
Lecture Notes
Recommended textbooks:
- John M. Lee, Introduction to Topological Manifolds, Springer, 2011
- L. M. Woodward and J. Bolton, A First Course in Differential Geometry, Cambridge University Press, 2019
Also suggested:
- S. Waldmann, Topology: An Introduction; Springer, 2014
- I.M. Singer, J.A. Thorpe, Lecture Notes on Elementary Topology and Geometry; Springer, 1977
- M. P. Do Carmo, Differential Geometry of Curves and Surfaces (2nd edition); Dover, 2016
Prüfung
Prüfung
Modul: 29.01.2020 9:00-12:00, Raum: Y03G91 Plätze: 90, Typ: schriftlich
Repetition: 27.08.2020 9:00-17:00, Raum: Y27H25 Plätze: 50, Typ: mündlich
