An introduction to homology (cont.) | Algebraic Topology 31 | NJ Wildberger
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users cite it when they are learning homology from the lecture itself or want an intuitive picture of cycles, boundaries and quotient groups, and then ask follow-up questions about specific steps.
Recommended by 1 people across 1 different months, 2014 to 2021.
What it is
A university-style lecture by Norman Wildberger, part 31 of his Algebraic Topology series, continuing the introduction to homology. He works with a simple graph and modifications to it, defines cycles, boundaries and chain groups as free abelian groups, and presents homology as cycles mod boundaries in each dimension.
What people said
Recommends Sooner · 2018-04 · Mathematics Stack Exchange · on “Questions about quotient space and homology”
I watched the lecture 31 of algebraic topology on youtube and could not figure out a problem. The link and the question picture are as follows: link: [this video] at time 21:32 [LINK] (In this picture the professor should wrote $c-d$ instead of $c+d$) The professor tried to say how to understand the homology means when a 2-cell is added to the 1-dim graph using a example as the picture shows. Before adding the 1-dim graph, I can understand the homology of the graph is just Z $\times$ Z because in this graph we can find two basic cycles ( or called generators). Then for every other cycles in this graph, we can represent it by the linear combinations of the two basic cycles. But when the professor
Cites dato datuashvili · 2014-02 · Mathematics Stack Exchange · on “understanding into algebraic terms difference between homology and cohomology”
my previous question understand quotient group [LINK] was related to understanding of quotient group,i dont need to know too much detailed in group theore,just some part of algebraic topology,especially my interest is to define Homology and Cohomology ,also intuittive understanding about their,what is different between them,may be it is wrong but i was looking for video about homology group in this video [this video] there was talking about cycles,kernels of cycles images, and was mentioned or represented Homology as a quotient of cycles and images,i have read also that Cohomology acts as a dual of homology,but what does mean dual term in group meaning?are Homology/Cohomology same besides only wi
Cites Kolmin · 2021-10 · Mathematics Stack Exchange · on “Basic Homology Question on Directed Graphs – Rules of Orientation”
SECOND EDIT: I start to understand (a bit) what is going on, but still an answer is much needed. Below I edited the question (along with the title) to point out the new little things I got. FIRST EDIT: I started a bounty on this question, for various reasons. First of all, because I really would like to get an asnwer. Also, I feel that it is really basic and many students could miss the same point. Finally, I feel all the books I consulted were not able to actually give me a proper answer. I was watching this video [this video] on youtube by Wildberger on Homology with the hope of understanding what this is all about and, as a matter of fact, I felt things where working fine. However, I do have a