Podcast
Questions and Answers
How can the cotangent bundle be described?
How can the cotangent bundle be described?
- As the same space as the cotangent space
- As the same bundle as the tangent bundle
- As the dual space of the cotangent space
- As the dual bundle to the tangent bundle (correct)
What is the cotangent bundle in differential geometry?
What is the cotangent bundle in differential geometry?
- The dual bundle to the tangent space
- The vector bundle of all the tangent spaces at every point in the manifold
- The vector bundle of all the cotangent spaces at every point in the manifold (correct)
- The dual bundle to the cotangent space
In what categories can the concept of cotangent bundle be generalized to?
In what categories can the concept of cotangent bundle be generalized to?
- Categories with more structure than smooth manifolds (correct)
- Categories with less structure than smooth manifolds
- Categories with only smooth manifolds
- Categories with only vector spaces
How is the cotangent bundle formally defined via diagonal morphism?
How is the cotangent bundle formally defined via diagonal morphism?
What gives an isomorphism between the cotangent bundle and the tangent bundle in the smooth case?
What gives an isomorphism between the cotangent bundle and the tangent bundle in the smooth case?
What gives an isomorphism between the cotangent bundle and the tangent bundle in the smooth case?
What gives an isomorphism between the cotangent bundle and the tangent bundle in the smooth case?
What is the cotangent bundle in differential geometry?
What is the cotangent bundle in differential geometry?
How may the cotangent bundle be described?
How may the cotangent bundle be described?
In the formal definition via diagonal morphism, what does the diagonal mapping Δ do?
In the formal definition via diagonal morphism, what does the diagonal mapping Δ do?
In what categories can the concept of cotangent bundle be generalized to?
In what categories can the concept of cotangent bundle be generalized to?
Flashcards are hidden until you start studying
