Universität Wien

250045 VO Contact Topology (2021S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

Sprache: Deutsch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

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

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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

Mindestanforderungen und Beurteilungsmaßstab

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).

Prüfungsstoff

The contents of the course.

Literatur

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

Zuordnung im Vorlesungsverzeichnis

MGEV

Letzte Änderung: Sa 23.09.2023 00:20