Talk:Betti number

Introduction

What makes some spaces more "reasonable" than others? Any statement about "the most reasonable finite-dimensional spaces" is inherently not mathematical. I suggest that the statement be made more clear/precise, or removed. — Preceding unsigned comment added by 132.64.72.154 (talk) 09:30, 27 August 2019 (UTC)

Relationship with differential forms

I think this subsection should not be here, or should be cut to one sentence. Tosha 03:40, 29 Apr 2004 (UTC)

Certainly the material could be added to the Hodge theory or de Rham cohomology pages instead; and links given instead.

Charles Matthews 06:50, 29 Apr 2004 (UTC)

Could someone at least put back in a link to De Rham cohomology? There are whole swathes of people interested in global analyis or electromagnetics for whom de Rham cohomology is the only algebraic topology they know hence know the Betti numbers as the dimension of these spaces and measuring 'how many closed forms are not exact' is a matter of vector calculus. Billlion 12:20, 20 Sep 2004 (UTC)

OK, fair enough. I've put the bare bones of why that works.

Charles Matthews 13:00, 20 Sep 2004 (UTC)

I think the first betti number of a general Pretzel is the number of the holes but not twice of it.BenlingLi 17:36, 20 October 2006 (UTC)

That's the genus g. B₁ = 2g for orientable surfaces. Charles Matthews 18:50, 20 October 2006 (UTC)

what is a "general Pretzel"? 24.58.63.18 (talk) 17:20, 20 February 2010 (UTC)

Images on triple torus will give you the idea. Charles Matthews (talk) 22:18, 20 February 2010 (UTC)

I understand that the origenal definition of a betti sequence of a manifold is that the kth term of the sequence is equal to the number of groups of homogenous k-dimentional submanifolds for that manifold. The examples in this artical do not seem to agree with this definition, unless either it is possible to have a submanifold of higher dimention than the origenal manifold or the first number listed is the 0th term of the sequence refering to 0 manifolds (points?). Is this definition obselete, or is it equivilent to the one given here? —Preceding unsigned comment added by 194.83.233.25 (talk) 11:59, 4 January 2008 (UTC)

More examples?

Can we have more examples of computed Betti numbers? e.g. RP2, RP3, CP2, S^2, S^3, full torus?.. Commentor (talk) 01:44, 13 March 2008 (UTC)

I've restored a section

That was deleted here [1]. It seems to be correct. 188.27.81.64 (talk) 21:20, 16 July 2014 (UTC)

Example

Hello. is the example for the simplicial complex correct? It seems to me that if the shaded region is the 2-simplex, then the hole is the non-shaded region. 147.26.87.13 (talk) 15:56, 25 July 2014 (UTC)

Last section

The last section looks like advertisement for some random biology paper. probably inappropriate in wikipedia in general, and on this page in particular. 134.157.10.42 (talk) 13:26, 20 July 2015 (UTC)

I deleted all but the link to Topological data analysis — Cheers, Steelpillow (Talk) 09:35, 21 July 2015 (UTC)

affine lie groups

Enquiring minds want to know: what are the Betti numbers for the affine Lie groups? Err quantum groups, from the affine Lie algebras? 203.210.8.148 (talk) 02:47, 26 October 2015 (UTC)

Betti Number of Finite Abelian Groups

I can not find the description for the Betti number for finite abelian groups. Should I add it to this article or have a separate article? Digital27 (talk) 17:44, 23 May 2024 (UTC)