Algebra for Homology: A Resource Guide

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SUMMARY

The discussion centers on the need for algebraic resources to support the study of homology, specifically referencing Vick's Homology. The user, Kevin, seeks guidance on understanding the technique of factoring a map through another space and requests recommendations for books focused on algebra relevant to algebraic topology. A suggestion is made to consult "Algebraic Topology" by Artin and Braun, which provides a comprehensive algebraic background, along with free online resources on modules.

PREREQUISITES
  • Understanding of basic algebra concepts, including direct sums and tensors.
  • Familiarity with algebraic topology principles, particularly homology.
  • Knowledge of mapping techniques in topology.
  • Basic understanding of modules in algebra.
NEXT STEPS
  • Research "Algebraic Topology" by Artin and Braun for foundational algebra concepts.
  • Explore free online resources on modules to strengthen algebraic understanding.
  • Study the technique of factoring maps in topology for practical application.
  • Investigate additional algebraic topology texts that avoid category theory for focused learning.
USEFUL FOR

Students and researchers in algebraic topology, particularly those seeking to strengthen their algebra skills to better understand homology and related concepts.

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Hello all,

So I'm working through Vick's Homology and have just finished up chapter one except that I have become aware of some holes in my algebra. Vick used and is beginning to use the idea of factoring a map through another space. While I can see the contextual meaning of the technique in the context of the problem, I'm not familiar with the technique in general.
So first, what's a good reference for that, and secondly, is there a book about "algebra for algebraic topology" you know, lots of direct sums, factoring, gradings, tensors, etc. It need not play with category theory. In fact I'd like to avoid the category stuff for a bit longer (trying to focus on the topology end of things for the moment).

As always thank you for any input,

kevin
 
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try the little alg top book by artin and braun, which is mroe complete in algebraic background.or any of the free algebra books on the web on modules.
 

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