<p>What would be the best Graduate Schools for Topology. Are their any Professors that are cutting edge in this field.</p>
<p>There must be. I don’t know much about the field besides that my friend’s father wrote a book about the subjec with 2 other people and dedicated it to her. He is a professor at the best Turkish university. Most people on this board won’t know what topology is.</p>
<p>Any of the math students should be familair with topology, it’s a fairly wide area of math so there are lots of professors doing research in many different areas of topology. Berkeley is very good for graduate school in math if you can get in.</p>
<p>Topology can hardly be defined as a wide area of math. Yes, most if not all math majors will know about its existence and perhaps even have some baisc knowledge of it, but would they know where good grad departments are?</p>
<p>Topology is a fairly broad field in terms of current research it’s definitely not narrow as a graduate student it’s one of the basic courses you take in your first year. </p>
<p>I’m assuming that the math undergraduate students here are among the best and so they should have a good knowledge of current mathematical research areas including topology and analysis since those are some of the most fundamental areas of pure mathematics. </p>
<p>Most undergraduates probable don’t know what the best departments are, the math professors do have a very good idea of who is doing research in their field i.e. topology. So the best way to get a good feel for what departments are good is to ask a professor who does active research in topology i.e. goes to conferences and publishes papers.</p>
<p>I agree with you in that math professors are the best source, but that one should ask many, not just one or a few, to get an opinion which is more accurate.</p>
<p>I would talk to some professors if I were you (especially a topology professor if your school has one). While it can also be beneficial to ask undergraduates who are applying to graduate school, this is not always a good way to find out all of them. For example, I’m not interested in any schools that aren’t in the Northeast USA or Southern California. And I would assume other students have geographical preferences, as well as others, that would limit their knowledge of schools.</p>
<p>Princeton has historically been good for topology.</p>
<p>As people have already said topology is a wide field: Set-theoretic topology, algebriac topology, differential topology etc. However all of these subfields have nontrivial intersection.
One of the most important development in topology in recent years is the connection with algebraic geometry via development of what is called motivic homotopy theory. This is what I would call cutting edge (Voevodsky got a fields medal for it in 2002). So if you want to work on this kind of stuff you might want to look at recent publications in the area to get an idea who is working on that kind of stuff.<br>
In general there are many universities who are rather strong in topology and it really depends on your particular interests which of them are good for you.</p>