Differential Topology Notes - at undergraduate level

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SUMMARY

The discussion centers on the challenges of finding undergraduate-level resources for Differential Topology, specifically noting the lack of dedicated textbooks in this area. Participants recommend Guillemin and Pollack's "Differential Topology" as a standard text used in some undergraduate programs. Additionally, a link to Hicks' notes is provided, which leans more towards differential geometry. The consensus highlights the need for supplementary online lecture notes that include diagrams and examples.

PREREQUISITES
  • Understanding of basic topology concepts
  • Familiarity with differential geometry principles
  • Knowledge of smooth manifolds
  • Ability to interpret mathematical diagrams and examples
NEXT STEPS
  • Research Guillemin and Pollack's "Differential Topology" for foundational knowledge
  • Explore online lecture notes and resources on Differential Topology
  • Study Hicks' notes on differential geometry for supplementary material
  • Investigate additional textbooks on differential geometry for broader context
USEFUL FOR

Undergraduate students in mathematics, educators seeking teaching resources, and anyone interested in enhancing their understanding of Differential Topology and its applications.

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I am trying to understand Differential Topology using several textbooks including Lee's book on Smooth Manifolds.

I am looking for some good online lecture notes at undergraduate level (especially if they have good diagrams and examples) in order to supplement the texts ...

Can anyone help in this matter ...

Peter
 
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Hi Peter,

In my opinion, there really isn't an 'undergraduate level' textbook in differential topology (there are however more undergrad textbooks in differential geometry). Some undergraduate programs use Guillemin and Pollack's Differential Topology as the standard textbook. Here is another text, but more on the side of differential geometry.

http://www.wisdom.weizmann.ac.il/~yakov/scanlib/hicks.pdf
 
Euge said:
Hi Peter,

In my opinion, there really isn't an 'undergraduate level' textbook in differential topology (there are however more undergrad textbooks in differential geometry). Some undergraduate programs use Guillemin and Pollack's Differential Topology as the standard textbook. Here is another text, but more on the side of differential geometry.

http://www.wisdom.weizmann.ac.il/~yakov/scanlib/hicks.pdf
Thanks for the advice and help, Euge ...

Peter
 

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