Appendix C.3: Construction of the manifold of mappings
Channel: Alexander Schmeding
Date: 2020-10-06

In this video we construct the manifold of mappings for mappings from a compact manifold to a manifold which admits a local addition. We shall then sketch the proof that this manifold structure is a canonical manifold of mappings. Furthermore, we discuss the tangent bundle of the manifold of mappings. Here the exponential law provides a convenient identification of the tangent bundle with a manifold of mappings. 

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/).