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Smooth Manifolds - Lee

This class was created by Brainscape user Andrew Frohmader. Visit their profile to learn more about the creator.

By: Andrew Frohmader
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Decks in this class (10)

Chapter 1 - Smooth Manifolds
Define topological manifold,
Define coordinate chart centered ...,
Basic examples of smooth manifolds
16  cards
Chapter 2 - Smooth Maps
Define smooth function f m r k c ...,
Let u be an open submanifold of r...,
Show that if f m n is smooth then...
19  cards
Chapter 3 - Tangent Vectors
Define geometric tangent space to...,
Discuss point derivations wrt r n...,
Let m be a smooth manifold with o...
19  cards
Chapter 4 - Submersions, Immersions, and Embeddings
What is the most essential proper...,
Define rank of f m n at p constan...,
Prove if dfp is surjective then p...
21  cards
Chapter 5 - Submanifolds
Define embedded submanifold codim...,
What are the embedded submanifold...,
What is relationship between smoo...
22  cards
Chapter 6 - Sard's Theorem
Define measure zero in r n measur...,
What is sard s theorem immediate ...,
What is whitney embedding theorem...
5  cards
Chapter 7 - Lie Groups
Define lie group left right trans...,
Key property of lie groups,
Examples of lie groups
23  cards
Chapter 8 - Vector Fields
Define vector field on m smooth r...,
How does smoothness of component ...,
Examples of vector fields
28  cards
Chapter 9 - Integral Curves and Flows
Define integral curve starting point,
Examples of integral curves globa...,
How does finding integral curves ...
22  cards
Chapter 10 - Vector Bundles
Define vector bundle smooth vecto...,
Discuss the mobius bundle,
Prove the tangent bundle is a vec...
19  cards

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Smooth Manifolds - Lee

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