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an informal student seminar.
Image of Hopf fibration by Richard Hennigan.
Summary
Summary
This is a seminar on the geometric topology of 3-manifolds organized by students for students, mainly aiming at master and PhD students. Of course, anyone who is interest is welcome to come.
Poincaré's homology sphere, taken from W. Threlfall and H. Seifert 's classic "Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes".
Main goals of the seminar
Main goals of the seminar
The idea is to break the seminar down into three parts. First, we intend to cover the basic topology of 3-manifolds, mainly the prime decomposition theorem, the JSJ decomposition theorem and the classification of Seifert manifolds. Second, we would focus in the geometry of 3-manifolds with the goal of understanding the eight model geometries, the statement of Thurston's geometrization conjecture (proved by Perelman) and go a bit deeper into hyperbolic geometry. Finally, the third part will consist on selected topics geometric topology, chosen by the participants of the seminar depending on what was found to be more interesting.
Statement of purpose
Statement of purpose
Our idea in the creation of this seminar was to give an overview and basis to the geometric topology of 3-manifolds. So, in principle, our talks should be centered on getting the big ideas, definitions, examples and theorems across without being too technical. In this seminar we are all learning the material, so there should be no expectation of impecable presentations and mastery of the material. After each talk, a forum-type meeting will follow where we can expand on what has been explained and maybe focus less on the big picture and more in details.
Format of the lectures
Format of the lectures
Each week there will be a lecture by a student with the standard duration of ninety minutes. Afterwards, there could be a little coffee break and another session focused on question or more technical aspects for those of us interested in more than a taste of geometric topology. This can either be based on the lecture given in the same day or the one before (in order to give ourself some studying time), this is yet to be determined.
Ideally, we would love that this second session turned into a (sort of) social event where we discussed our questions and cute ideas of the topics at hand.
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