Tagging - 2019-04-15

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3:46 AM

new-tag A new tag cellular-homology was created by Ignorant Mathematician.

I am giving $S^n$ the CW complex structure with $2$ $k-$cells in each dimension $0\leq k\leq n$ . The attaching maps are given by the pushout diagram. $\require{AMScd} \begin{CD} S^{k-1}\cup S^{k-1} @>{i}>> D^k\cup D^k\\ @V{id\cup id}VV @VVV \\ S^{k-1} @>>> S^k \end{CD} $ I want to compute the...

Cellular homology

In mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can provide an effective means of computing homology modules. == Definition == If X {\displaystyle X} is a CW-complex with n-skeleton X n {\displaystyle X_{n}} , the cellular-homology modules are defined as the homology groups of the cellular chain complex ⋯ → ...

2 hours later…

Arctic Char

5:41 AM

I have edited away the tag "cellular homology". Given that we already have "homology-cohomology" and "cw-complex", I think it already covers the subject well.

Andrews

6:34 AM

I have a question in tag differential-geometry, is that tag only focus on classical differetial geometry?

I mean the study of curves and surfaces, typical content includes curvature and frames of curves and surfaces, 1st and 2nd fundamental form of surfave, Gauss-Codazzi equation and Gauss theorem etc.

Arctic Char

@Andrews No, definitely not. The tag is used for study in all dimensions, and include Riemannian geometry etc. If the question is about surface, one can use also the "surface" tag.

Andrews

Is tag differential-geometry too broad to contain both study of smooth manifolds and study of fiber bundles and geometric analysis?

BTW, there's no such tag geometric-analysis in MSE, there's one in MO

Arctic Char

Basically now all questions in Geometric analysis are tagged either DG or RG, or both. That's fine.

Andrews

That's why I'm wondering if tag differential-geometry is too broad, although I admit differential geometry does contain lots of contents.

11 hours later…

Arnaud D.

6:15 PM

@Andrews I think it's fine for a tag to be very broad. Tags such as real-analysis, abstract-algebra, algebraic-geometry or algebraic-topology also cover a lot of contents, but they are useful to delimit the subject of a question.

Although I guess it is possible for a tag to be too broad. My understanding is that analysis and algebra used to exist here, but have since been "fragmented" into several slightly more specific tags.

And now that I actually checked, it seems that the situations are slightly different : algebra has been black-listed, but analysis still exists but the tag-excerpt suggest using the more specific tags instead.

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