String theory - Homology and Homotopy

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SUMMARY

This discussion focuses on the relationship between Homology, CoHomology, and Homotopy groups, with specific reference to the Hurewicz Theorem. Lala expresses a need for a deeper understanding beyond the physicists' treatment of the subject. Alan Hatcher's book, available on his Cornell site, is recommended for its comprehensive yet challenging approach to algebraic geometry, which aids in grasping these concepts. For a less detailed introduction, Nakahara's work is suggested, although it lacks the depth of the Hurewicz theorem.

PREREQUISITES
  • Understanding of Homology and CoHomology concepts
  • Familiarity with Homotopy groups
  • Knowledge of the Hurewicz Theorem
  • Basic principles of algebraic geometry
NEXT STEPS
  • Study Alan Hatcher's book on algebraic topology for a detailed understanding of Homology and Homotopy
  • Explore Nakahara's text for a physicist's perspective on algebraic geometry
  • Research the implications of the Hurewicz Theorem in algebraic topology
  • Investigate the connections between algebraic geometry and string theory
USEFUL FOR

Mathematicians, physicists, and students of algebraic topology seeking to deepen their understanding of the relationships between Homology, CoHomology, and Homotopy groups.

wodhas
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Hi,

I am trying to understand relations between Homology/CoHomology and Homotopy group..I am familiar with Hurewicz Theorem but I need something more general.

I hope that you can help.

Thanks,
Lala
 
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I didn't understand the physicists treatment of the subject at all when I was first learning about it as an undergrad. So instead I took an algebraic geometry class in the math department, and well things became a lot clearer.

We used Alan Hatchers book (which you can find online at his Cornell site). Be warned, its quite opaque and difficult, but then once you get it, the physics stuff is relatively trivial by comparison and it has a pretty good review off the particular question you are asking.

If that's too much, then typically physicists learn their algebraic geometry from something like Nakahara, but then it won't get into the nitty gritty details of stuff like the Hurewicz theorem.
 

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