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Results tagged with intuition
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user 4991
Questions asking for the intuition behind some definition, conjecture, proof etc. In other words, questions designed to improve or to acquire understanding on a conceptual or intuitive level, as opposed to on a technical or formal level. When asking such a question it can be helpful to include a rough description of ones understanding of the subject at hand (on a technical level).
10
votes
What is the difference between homology and cohomology?
On a closed, oriented manifold, homology and cohomology are represented by similar objects, but their variance is different and there is an important change in degrees. For simplicity, consider homol …
40
votes
Why does one think to Steenrod squares and powers?
Here's how I explain Steenrod squares to geometers. First, if $X$ is a manifold of dimension $d$ then one can produce classes in $H^n(X)$ by proper maps $f: V \to X$ where $V$ is a manifold of dimens …
- 4,990
9
votes
how do you visualize characteristic class?
This is a variation on standard answers (to this standard question). I'll start with a bit of philosophy since you mentioned different ways to think of cohomology. Singular cohomology is fairly "tra …
- 4,990