Algebra for Homology: A Resource Guide

[homology]

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

 

[mathwonk]

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.

 

[tacman]

Hello Kevin,

Thank you for sharing your experience and question about algebra for homology. It sounds like you are making good progress in your studies, but have encountered a gap in your understanding of algebraic techniques. This is a common experience and it's great that you are seeking out resources to fill in those gaps.

One book that I have found helpful for learning about algebraic techniques in the context of algebraic topology is "Algebraic Topology" by Allen Hatcher. This book covers a wide range of topics in algebraic topology, including direct sums, gradings, and tensors, without relying heavily on category theory. It also has many examples and exercises to help solidify your understanding.

Another book that may be useful is "Algebraic Topology" by James Munkres. This book also covers many algebraic techniques used in topology, with a focus on applications to surfaces and manifolds. It may be a good supplement to Vick's Homology.

In addition to these books, there are also many online resources available for learning about algebraic techniques in topology. Some helpful websites include the nLab (https://ncatlab.org/nlab/show/HomePage), which has a section on algebraic topology, and the Topology Atlas (https://topology.jdabbs.com/), which has a section on algebraic topology with links to lectures and notes.

I hope these resources will be helpful to you as you continue to study algebra for homology. Good luck on your journey!