References for Self Study in de Rham Cohomology

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SUMMARY

The discussion focuses on self-study resources for de Rham cohomology, specifically in relation to Guillemin and Pollack's book, "Differential Topology." The user seeks alternative references that align closely with the definitions used in Guillemin and Pollack. Recommended resources include chapters 7-8 of Spivak's "Differential Geometry, Vol. 1" and chapters 4-5 of Singer and Thorpe's "Lecture Notes on Elementary Topology and Geometry." These references are suggested to help overcome challenges in the exercises presented in Guillemin and Pollack's text.

PREREQUISITES
  • Familiarity with de Rham cohomology concepts
  • Understanding of differential topology principles
  • Knowledge of Spivak's "Differential Geometry, Vol. 1"
  • Acquaintance with Singer and Thorpe's lecture notes
NEXT STEPS
  • Explore chapters 7-8 of Spivak's "Differential Geometry, Vol. 1"
  • Review chapters 4-5 of Singer and Thorpe's "Lecture Notes on Elementary Topology and Geometry"
  • Investigate additional online course notes on de Rham cohomology
  • Study alternative texts that align with Guillemin and Pollack's definitions
USEFUL FOR

Mathematicians, graduate students in topology, and anyone studying de Rham cohomology who seeks resources that align with Guillemin and Pollack's approach.

MissMoneypenny
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I've been trying to self study the section on de Rham cohomology in Guillemin and Pollack's book Differential Topology. The section is in a sense hands on: most of the results are presented as exercises scattered throughout the section, and some hints are given. I've hit a road block in a few of the exercises and have been searching for a book, some online course notes or some other reference on de Rham cohomology to help me through the exercises I'm stuck on. However, Guillemin and Pollack use slightly different definitions than all of the other books or notes I've been able to find. I'd like to find a book, set of notes, or some other reference that uses similar definitions to Guillemin and Pollack. Can anyone who is familiar with Guillemin and Pollack's book point me in the direction of an alternate reference that treats de Rham cohomology in a similar manner to GP? Thank!
 
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try chapters 7-8 of spivak's differential geometry vol. 1, or chapters 4-5 of singer and thorpe's lecture notes on elementary topology and geometry.
 
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mathwonk said:
try chapters 7-8 of spivak's differential geometry vol. 1, or chapters 4-5 of singer and thorpe's lecture notes on elementary topology and geometry.
Thanks a lot for your suggestions. I'll head to the library and have a look at those books.
 

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