Department Mathematik



Thomas Vogel

Mathematisches Institut
Differentialgeometrie und Topologie
Ludwig-Maximilians-Universität München
Theresienstr. 39
80333 München
Zimmer (room): 314

phone: 089 2180 4625
email : name (at)
           Ersetze (replace) name durch (by) tvogel
Sprechstunde: nach der Vorlesung am Dienstag oder Donnerstag

Preprints/Articles :

  • On the asymptotic linking number, Proc. Amer. Math. Soc. 131 (2003), 2289-2297. (pdf)
  • mit D. Kotschick , Linking numbers of measured foliations, Ergodic theory and Dynam. Systems 23 (2003), 541-558. (pdf)
  • A construction of Engel structures, C. R. Acad. Sci. Paris, Ser. I 340 (2005), 43-48. (pdf)
  • Existence of Engel structures, Annals of Math. (2), 169 (2009), 79-137.   (pdf)
  • Maximally non-integrable plane fields on Thurston geometries, IMRN Nr. 21 2006, Article ID 97315   (pdf)
  • mit S. Baader und K. Cieliebak , Legendrian ribbon knots in overtwisted contact structures, JKTR 18 (2009), 523-529.   (pdf)
  • Rigidity versus flexibility for tight confoliations, Geometry and Topology 15 (2011) No. 1, 41-121 (journal)
  • Uniqueness of the contact structure approximating a foliation, Geometry and Topology 20 (2016), no.5, p. 2439-2573. (journal)
    Here is a version of this preprint with fewer typos and slightly more details (the mathematical content is the same as in the arxiv-version).
  • mit D. Kotschick Engel structures and weakly hyperbolic flows on four-manifolds, Comm. Math. Helv. 93 (2018), 475-491, (pdf) .
  • Non-loose unknots, overtwisted discs and the contact mapping class group of S3, Geom. Funct. Anal. 28 (2018), no. 1, 228-288, (pdf) .
  • mit A. del Pino, The Engel-Lutz twist and overtwisted Engel structures, (pdf), to appear in Geometry and Topology.
  • mit V. Colin, F. Presas, Notes on open book decompositions for Engel structures, (pdf) ,, to appear in Alg. & Geom. Topology 18-7 (2018), 4275-4303.

Vorlesungen/ Übungen/ Seminare

Sommer 2023

  • Mengentheoretische Topologie
    • Vorlesung: Di, 12:00-13:30 Do, 12:00-13:30 Raum A027
    • Sprache/Language: Both English and German are possible.
    • Übungen: Mi, 14-16 B004 mit Lukas Böke.
    • Inhalt: Viele von den Dingen die im Zyklus Algebraische Topologie unter den Tisch fallen, z.B. Konstruktion stetiger Funktionen, Metrisierbarkeit, uniforme Räme, etc.
    • Zielgruppe: Bachelor/Master Mathematik. Vom Niveau irgendwo zwischen dem vierten und sechsten Semester. Lehramtsstudenten sind willkommen, ich weise aber darauf hin dass diese Vorlesung die GTF-Vorlesung nicht ersetzt.
    • Es gibt eine Moodle Seite, der Einschreibeschlüssel ist Pavel. Urysohn and Alexandrow are two Pavels who have founded topology.
  • Seminar: Morse Theory
    Date/Room: Tuesday, 10-12 Room B134
    Organizational meeting: second week of term, April 25.
    There is a moodle page. They key to enroll yourself is Marston. Content will follow soon.
  • Obeseminar: Geometrie
      Date/Time: Tue 4-6pm, Room B252.

Winter 2022/23

  • Symplectic Geometry 2
    Vorlesung/Lecture: Tue, 12-14 Thu, 12-14 in Room A027
    Prerequisites: Clearly, having attended Symplectic Geometry 1 is ideal, but I will try to make the lecture accessible for those who didn't.
    There is a moodle page . The key to enroll yourself is Vladimir (the first name of one of the pioneers of the field).
  • Seminar: Geometrie
    Termin: Do, 14-16 in B252
    Insbesondere Studierende des Lehramts Gymnasium sind willkommen.
    Das Seminar hat eine Moodle-Seite. Das Passwort zur Selbsteinschreibung ist Samos, die Insel auf der Pythagoras geboren wurde. Die Zahl der Teilnehmer ist auf 30 limitiert. Die Moodle Seite wird sich hoffentlich bald mit Inhalten füllen.
  • Blockseminar (mit Uli Bauer (TUM)): Combinatorial Torsions
    Termin: 27.-31. Maerz 2023
    Programmentwurf (pdf) Anmeldung/Registration via this moodle page. The key to inscribe yourself is Kurt, the first name of Kurt Reidemeister.
  • Oberseminar
    Termin: Di, 16-18 Uhr HS B252

Summer 2022

  • Topology 2
    Vorlesung/Lecture: Tue, 12-14 Thu, 12-14 in Room B132
    Exercise classes: Wed, 14-16 in Room B143.
    Prerequisites: Clearly, having attended Topology 1 is ideal, but I will try to make the lecture accessible for those who didn't. To this end, we will start with applications of singular homology thereby revising the required material. >br> There is a moodle page. The key to enroll yourself is Heinz (the first name of one of the pioneers of algebraic topology).
  • Oberseminar
    Termin: Di, 16-18 Uhr HS B252
  • Seminar : Knoten/knots
    Time: Thu, 14-16, B039
    Organizational meeting on April 28
    There is a moodle page. The key to enroll yourself is Kurt (the first name of Reidemeister, who defined elementary moves on knot diagrams).

Winter 2021/22

  • Topology 1
    Vorlesung/Lecture: Tue, 12-14 Thu, 12-14 in Room B005
    Exercise classes: Wed, 8-10 in Room B005.
    There is a moodle page. The key to enroll yourself is Henri (the first name of one of the founders of algebraic topology).
    Lectures will be in English. For now, the lecture will be in a lecture room following the rules outlined here. (I plan to make use the right to check compliance with 3G-rules occasionally). I will provide lecture notes.
  • Oberseminar
    Termin: Di, 16-18 Uhr HS B252
  • Seminar : Morse theory
    Time: Thu, 14-16, definitely online.
    Again, here is a moodle page. The key to enroll yourself is Marston (one of the first names of Mr. Morse)
    We will study Morse theory on manifolds and a discrete version of it. The required knowledge is not heavy, mostly multivariable calculus. Having attended a lecture on differentiable manifolds would be great but is not strictly necessary. This seminar is joint with Uli Bauer .

Summer 2021

  • Riemannian Geometry
    Vorlesung/Lecture: Tue, 12-14 Thu, 12-14
    Exercises with Lukas Böke on Wednesday, 8-10, also via Zoom
    There is a moodle page. The moodle key is Weyl.
    Lectures will be on Zoom in English.
  • Reading course on Riemann surfaces
    tentative time: Thu, 10-12.
    Our goal is the uniformization theorem, via harmonic functions. We will try have discussions lead by varying participants. The hope is that this format is better suited for the current circumstances than an online seminar. If you are interested, please send an email to me. Thanks.

Winter 2020/21

  • Differentiable manifolds with Ivo Sachs
    Vorlesung/Lecture: Tue, 10-12 Uhr, Thu, 10-12 Uhr
    So far, I have been not very successful with moodle. The videos of lectures before Christmas (By T. Vogel) can be found here, the videos of the sond half (I. Sachs) are here. of the lecture can be accessed through this website. Übungen/Exercise classes:
    Due to the current circumstances the lecture and the exercise classes will be via Zoom. Exams will be a take home exam, the date has still to be determined.
    Please register here before November 5, 2020. The lecture can be found as a lecture in physics (elective courses at master level) or as a lecture in mathematics (bachelor level). Somebody has assigned the number 16243 to the course. After November 5, or if you are not a student of LMU, please send an email.

Winter 2019/20

  • Differentiable manifolds
    with Ivo Sachs
    Vorlesung/Lecture: Di, 10-12 Uhr B005 , Do, 8-10 Uhr, B006
    More information can be found here.
  • Contact topology
    with Yang Huang
    Time, place: Wednesday, 16-18 in B006
    Notes: (pdf)
  • Seminar: Knotentheorie
    Zeit, Ort: Mittwoch, 14-16 in B039
    Vorbesprechung: Mittwoch, 16. Oktobver, 14:30
    Zielgruppe: Bachelor, Lehramt (vertieft) Mathematik
    Program: (pdf)
  • Oberseminar
    Termin: Di, 16-18 Uhr HS B252

Summer 2019

  • Geometrie und Topologie von Flächen
    Vorlesung: Mi 14-16 Uhr , Do, 12-14 Uhr, jeweils im Hörsaal 138
    Im LSF sind Zentralübung und die Vorlesung am Freitag vertauscht.
    Zentralübung: Fr 12-14 Uhr, Hörsaal 138
    Tutorien und Aufgaben : Info
    Skript von Prof. T. Hoffmann zu Rotationsflächen konstanter Krümmung.
    Kurzskript: (pdf)
    Klausur: Montag, 29. Juli, 16-20 Uhr in Hörsaal B051, B052, B005 (nach Anfangsbuchstben des Nachnamens)
    in der Theresienstr. 39
    Es sind keine Hilfsmittel zugelassen.
    Nachholklausur: Donnerstag, 10. Oktober, 9-12 Uhr im Hörsaal M218 im Hauptgebäude (Geschwister-Scholl Patz)
    Eine Wiederholung zur Notenverbesserung ist in der PO2015 für Bachelor Mathematik explizit ausgeschlossen. Im Lehramt spielt Sie für die Zulassung zum Staatsexamen keine Rolle. Ihr Beitrag zur Endnote (LPO I Par 3 und 4, sowie Par. 14 der Prüfundordnung) liegt im Prozentbereich. Daher lassen wir die Wiederholung zur Notenverbesserung auch im Lehramt nicht zu.
  • Seminar: Atiyah-Singer index theorem
    Time, place: 12-14 on Wednesday's in Room B045.
    Organizational meeting on Wednesday, April 24th.
    Program: (pdf)

Winter 2018/19