Institute of Mathematics

Lecture courses/details

Fall 18

Geometrie / Topologie

Speaker: Alberto Cattaneo

Lectures

Mo 10.15 - 12.00
Room: Y16G05
We 10.15 - 12.00
Room: Y03G91

Exercises

We 08.00 - 09.45
Y23G04
Übungen Geometrie / Topologie Gr.1
Tutor: Nima Moshayedi
Th 13.00 - 14.45
Y34F01
Übungen Geometrie / Topologie Gr.2
Tutor: Nicola Capacci
Fr 13.00 - 14.45
Y27H25
Übungen Geometrie / Topologie Gr.3

Course Description

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


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

Exam

Module: 29.01.2020 9:00-12:00, Room: Y03G91, Type: written exam

Module: MAT701 Geometrie / Topologie I