Differential Geometry

Differential geometry is for many reason a very important branch of matematics and has many uses throughout physics.

I have tried to learn it well many times but every time I have met some kind of obstacle in the form of hard concepts or time available.

I am now again trying to learn the subject together with Lie and representation theory in order for me to better understand QFT and modern physics.

Current challenges

• Differential forms vs covectors
  • why the alternating structure for differential forms
  • are there other forms than the ones representable as differential forms
  • if not, why is there not also an alternating structure on the tangent spaces and only on the cotangent spaces