Infinite-dimensional geometry 1.3 Part 2: Tangent spaces and the tangent bundle
Channel: Alexander Schmeding
Date: 17/09/2020

We define for a (possibly infinite-dimensional) manifold the geometric tangent space (aka the kinematic tangent space) and show that these spaces give rise to a vector bundle, called the tangent bundle, over the base manifold. Further, tangent mappings of differentiable mappings between manifolds are discussed.

This is part of the course MAT331: Topics in Analysis at the University of Bergen in Fall 2020. 
This course (and the lecture) was supported by Trond Mohn foundation within the Pure Mathematics in Norway program (https://www.puremath.no/).