What are some recommended resources for practicing problems on smooth manifolds?

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SUMMARY

The discussion centers on recommended resources for practicing problems related to smooth manifolds, specifically referencing "Intro to Smooth Manifolds" by John M. Lee. Participants suggest several alternative texts, including "An Introduction to Manifolds" by Loring W. Tu, which is noted for its gentler approach, and "Topology from the Differentiable Viewpoint" by John Milnor, praised for its concise and intense content. Other notable mentions include works by Spivak, Lang, and Warner, which also cover similar material. The community seeks additional problem sets beyond Lee's book.

PREREQUISITES
  • Familiarity with smooth manifold theory
  • Understanding of differential topology concepts
  • Basic knowledge of algebraic topology
  • Experience with mathematical problem-solving techniques
NEXT STEPS
  • Explore "An Introduction to Manifolds" by Loring W. Tu for additional problems
  • Study "Topology from the Differentiable Viewpoint" by John Milnor for concise insights
  • Investigate problem sets available online for smooth manifold theory
  • Read "Differentiable Forms in Algebraic Topology" for advanced problem-solving
USEFUL FOR

Mathematicians, graduate students in mathematics, and anyone seeking to deepen their understanding of smooth manifolds and enhance their problem-solving skills in this area.

ForMyThunder
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Right now, I'm reading through Lee's Intro to Smooth Manifolds and I was wondering if there is a website somewhere that has problems different from the book. Or if there is another book out there that covers about the same material as Lee's that would be good to.

Thanks in advance.
 
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There are many many books about smooth manifold theory. Just browse amazon.com.

The book An Introduction to Manifolds by Tu is actually even more gentle than Lee. Less gentle but still good are Spivak, Lang, Warner just to name a few.
 
ForMyThunder said:
Right now, I'm reading through Lee's Intro to Smooth Manifolds and I was wondering if there is a website somewhere that has problems different from the book. Or if there is another book out there that covers about the same material as Lee's that would be good to.

Thanks in advance.

A good companion book is Milnor's Topology from the Differentiable Viewpoint. a short intense book. Many methematicians esteem it. It has good problems at the end.

Differentiable Forms in Algebraic Topology is a hard book but incredibly good.
 

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