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4 - Differentiable Manifolds

Published online by Cambridge University Press:  08 December 2022

Esko Keski-Vakkuri ,
Claus Montonen  and
Marco Panero
Esko Keski-Vakkuri
Affiliation:
University of Helsinki
Claus Montonen
Affiliation:
University of Helsinki
Marco Panero
Affiliation:
Università degli Studi di Torino, Italy
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Summary

We introduce basic topological concepts, which are used to define continuous mappings, and topological invariants. Next, we introduce a differential structure on manifolds, to extend calculus from Euclidean spaces to the more general setting of differentiable manifolds.

Keywords

Topologyhomotopydifferentiable manifoldsdifferential formssymplectic geometry
Type
Chapter
Information
Mathematical Methods for Physics
An Introduction to Group Theory, Topology and Geometry
 , pp. 99 - 169
Publisher: Cambridge University Press
Print publication year: 2022

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