Seminar: Ricci flow, Part II
Prof. Bernd Ammann, Zimmer 119
Time and Place
Mon 8-10, M102
Please register by email.
Please also register in G.R.I.P.S., as we send announcements
via this system.
Content of the Seminar
In this seminar we will study the Ricci-flow in arbitrary dimensions.
The Ricci flow in dimension 3 provides the geometrisation of
compact oriented 3-manifolds in the sense of Thurston.
This is a decomposition in elementary pieces. The Poincare conjecture is a
special case. One talk of the seminar will sketch this program.
Other topics are
shorttime existence and uniqueness of the flow,
the neckpinch and curvature evolution.
The goal is to understand the behavior of the flow until the blowup in
singularities and the entropy formula.
However, it is not realistic to give a full proof of the geometrisation
within this seminar.
Instead our aim is to acquire an overview over the central parts of the proof.
Program
The seminar program
is here as pdf-file.
The program of the previous semester is available here as pdf-file.
Related web sites
Literature
For a list of the literature directly related to the seminar,
please have a look at the program above.
Further literature
Disclaimer: this list is not up to date and by far not complete!
- S. Brendle; Ricci Flow and the Sphere Theorem, AMS Graduate Studies Vol. 111, 2010
-
C. Böhm; B. Wilking;
Manifolds with positive curvature operators are space forms.
Ann. of Math. (2) 167 (2008), no. 3, 1079--1097.
- M. Boileau; Geometrization of 3-manifolds with symmetries
- S. Brendle; R. Schoen;
Manifolds with 1/4-pinched curvature are space forms, J. Amer. Math. Soc. 22 (2009), 287-307.
Journal, ArXiv
- Brendle, Simon; Schoen, Richard; Curvature, sphere theorems, and the Ricci flow;
Bull. AMS. 48 (2011), 1-32, ArXiv
- S. Brendle; R. Schoen;
Classification of manifolds with weakly 1/4-pinched curvatures,
Acta Math. 200, 1--13 (2008), ArXiv
- Allen Hatcher: Notes on Basic 3-Manifold Topology 2000
- John Lott's Ricci-Fluss-Seite (Strongly recommended!)
- John W. Morgan, Gang Tian; Ricci Flow and the Poincare Conjecture
- J. Milnor; Towards the Poincaré Conjecture and the Classification of 3-Manifolds
- John W. Morgan: Recent progress on the Poincaré conjecture and the classification of 3-manifolds. Bulletin Amer. Math. Soc. 42 (2005) no. 1, 57-78 (expository article explains the eight geometries and geometrization conjecture briefly, and gives an outline of Perelman's proof of the Poincaré conjecture)
- J. Morgan; Frederick Tsz-Ho Fong Ricci Flow and Geometrization of 3-Manifolds. University Lecture Series. AMS (2010)
- G. Peter Scott, The geometries of 3-manifolds. (errata) Bull. London Math. Soc. 15 (1983), no. 5, 401-487.
- Peter Topping; Lectures on the Ricci flow
- Huai-Dong Cao, Xi-Ping Zhu; Hamilton-Perelman's Proof of the Poincaré
Conjecture and the Geometrization Conjecture
- Perelman's articles ArXiv 0211159,
ArXiv 0303109
and ArXiv 0307245.
Wikipedia-Page to the Ricci flow.
Formal requirements (in German)
Kriterien für benotete Leistungsnachweise
Um die üblichen Leistungsnachweise zu erhalten, sind folgende
Kriterien zu erfüllen:
- Erfolgreiches Vortragen
- Schriftliche Ausarbeitung eines Vortrages
- aktive Mitarbeit im Seminar
Unbenotete Leistungsnachweise
Wie bei benoteten Leistungsnachweisen.
Modulteilprüfung
Vortrag und Ausarbeitung bilden die Modulteilprüfung.
Bernd Ammann, 20.1.2017 oder später