Institut für Mathematik


Geometrie / Topologie

Dozent: Alberto Cattaneo

Program of the course
You are allowed to bring two A4 pages (= four sides) of handwritten notes to the exam.


Mo 10.15 - 12.00
Raum: Y16G05 Plätze: 30
Mi 10.15 - 12.00
Raum: Y03G91 Plätze: 25


Mi 08.00 - 09.45
Y23G04 Plätze: 20
Übungen Geometrie / Topologie Gr.1
Tutor: Nima Moshayedi
Do 13.00 - 14.45
Y34F01 Plätze: 14
Übungen Geometrie / Topologie Gr.2
Tutor: Nicola Capacci
Fr 13.00 - 14.45
Y27H25 Plätze: 20
Übungen Geometrie / Topologie Gr.3

Topology Notes
Euclidean and metric spaces

Topological spaces

Bases and manifolds


Products and disjoint unions


Adjunction spaces and topological groups



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

Plane curves


Tangent planes

The first fundamental form

More on the first fundamental form


Smooth maps

The derivative of a map

Conformal maps

Weingarten map and second fundamental form


Normal curvature

More on the curvatures

Theorema egregium

Theorema egregium II


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


Modul: 29.01.2020 9:00-12:00, Raum: Y03G91 Plätze: 25, Typ: schriftlich
Repetition: 27.08.2020 9:00-17:00, Raum: Y27H25 Plätze: 20, Typ: mündlich

Modul: MAT701 Geometrie / Topologie I