Universität Wien

250045 VO Contact Topology (2021S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

https://univienna.zoom.us/j/95644899647?pwd=V3NNTitXZGdmTWRLR0VVZ3JjNW10QT09

password: closed compact surface of genus 1 (same as for Algebraic Topology)

Thursday 04.03. 10:45 - 13:15 Digital
Thursday 11.03. 10:45 - 13:15 Digital
Thursday 18.03. 10:45 - 13:15 Digital
Thursday 25.03. 10:45 - 13:15 Digital
Thursday 15.04. 10:45 - 13:15 Digital
Thursday 22.04. 10:45 - 13:15 Digital
Thursday 29.04. 10:45 - 13:15 Digital
Thursday 06.05. 10:45 - 13:15 Digital
Thursday 20.05. 10:45 - 13:15 Digital
Thursday 27.05. 10:45 - 13:15 Digital
Thursday 10.06. 10:45 - 13:15 Digital
Thursday 17.06. 10:45 - 13:15 Digital
Thursday 24.06. 10:45 - 13:15 Digital

Information

Aims, contents and method of the course

Contact topology originated from Hamiltonian dynamics and optics in the 19th century. It enriches the topological structure of manifolds with a plane field and enables the study of e.g. phase spaces of
moving objects or thermodynamics. This lecture will provide an introduction to the rich theory of contact structures mostly on 3-manifolds. After introducing the basics we will talk about convex surfaces, Legendrian and transverse knots and open book decompositions.

Assessment and permitted materials

Oral exam (in case that presence examination is not possible then: online exam)

Minimum requirements and assessment criteria

This is an advanced course. Working knowledge of abstract manifolds, as well as some knowledge of Algebraic- and Differential Topology and Differential Geometry is required. (If you are in doubt please write me an email).

Examination topics

The contents of the course.

Reading list

books:
* Hansjörg Geiges, An introduction to contact topology
* Burak Özbağcı and András Stipsicz, Surgery on contact 3-manifolds and Stein surfaces

online resources:
* Expository articles by John Etnyre: Introductory lectures on contact geometry, Legendrian and transversal knots, open book decompositions and contact structures, and contact geometry in low-dimensional topology
* course notes of Patrick Massot:
Topological methods in 3-dimensional contact geometry

Association in the course directory

MGEV

Last modified: Sa 23.09.2023 00:20