Sorry for the somewhat qualitative question but what are the essential prerequisites for someone wanting to learn topological field theory from say the more physical side of things? The math side also sounds interesting but it may be a bit heavy going for my current background. I know quantum mechanics, some algebraic topology and some basic manifold theory. Here is the impression of what I have so far:

  • Path integral formulation of QFT
  • Differential Geometry including differential forms, bundles, cohomology theory etc
  • Yang-Mills/Chern-Simons gauge theories
  • Knot Theory and the Jones Polynomial

And for a more mathematical view:

  • Category Theory.

Baez's book "Gauge Fields, Knots and Gravity" seems to cover a good amount of these topics.

Am I on the right track or should I add/remove any topics from these? Thanks.

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    $\begingroup$ Hi lastone, and welcome to Physics Stack Exchange! Questions like this, about the mathematical prerequisites to a physical topic, are not really what this site is for, but you could suggest an edit to the TFT tag wiki that includes this information. $\endgroup$ – David Z Feb 1 '13 at 22:53
  • $\begingroup$ @DavidZaslavsky he obviosly does not have the information, so he can not suggest a meaningful edit to the the tagwiki ... The ones who ask, are not the ones who can put the information there, that would be the answerers. That is why I still disagree with the direct edits. It will never work unless you successfully launch a large campain to get actually the information needed into the tagwikis. People who possess the information will not put it there just like that such that people who need it, such as this OP, can retrieve it. We have a catch 22 and are stuck with not getting this info at all $\endgroup$ – Dilaton Feb 1 '13 at 23:19
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    $\begingroup$ Related: physics.stackexchange.com/q/41589/2451 $\endgroup$ – Qmechanic Feb 1 '13 at 23:19
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    $\begingroup$ @Dilaton did you notice the information you suggest the OP doesn't have is actually included in the question in this case? $\endgroup$ – David Z Feb 1 '13 at 23:25
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    $\begingroup$ Prequisite questions often fit poorly on Phys.SE. What can be said objectively about prequisites should be clear from consulting e.g. Wikipedia or the foreword of a textbook on the subject. More than that tends to be primarily opinion-based. $\endgroup$ – Qmechanic Jan 18 '14 at 1:48