Institut für Mathematik

Vorlesungen/Details

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.

Vorlesungen

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

Übungen

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

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

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