Functors in Differential Geometry.pdf

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Functors in Differential Geometry
De Waal Martijn - Smeenk Sebastiaan - Sitbon Pascal - Zacharopoulos Georgios
February 4, 2019
After presenting the notion of a category and providing some examples we focus towards the
cotangent bundle of a manifold. This space plays a very important role in symplectic geometry.
Indeed we will show that it is possible to give a symplectic structure on the cotangent bundle
in a canonical way. We present a functor between the category of smooth manifolds equipped
with diffeomorphisms (or local diffeomorphisms) and the category of symplectic manifolds
equipped with symplectomorphisms for which the object assignment consists of associating to
a space its cotangent bundle.