Talk:Density on a manifold

More detail on construction

While the construction given here is good enough for people familiar with associated bundles, I think it would be worthwhile being a bit more explicit. I suggest this because I am a research mathematician trying to get a more theoretical understanding of density bundles and the description given here took a me an hour or so to unravel. BenWhale (talk) 22:54, 7 July 2010 (UTC)

Even for someone familiar with the associated bundle construction, the current definition is incomprehensible. --81.99.202.66 (talk) 16:08, 27 March 2011 (UTC)

It gives the explicit cocycles. What more would you like to see? Sławomir Biały (talk) 22:01, 27 March 2011 (UTC)

The fibre of the s-density bundle at x∈M is the one-dimensional vector space consisting of functions μ:T_xM×...×T_xM→R that satisfy

$\mu (AX_{1},\ldots ,AX_{n})=|\det A|^{s}\mu (X_{1},\ldots ,X_{n})$

for every linear mapping A:T_xM→T_xM. I suppose this the end product of the cryptical construction. Gluing together the fibres is not explained here, of course, but perhaps something like this should be added to the article?Lapasotka (talk) 18:07, 22 June 2011 (UTC)

Sounds good. Sławomir Biały (talk) 19:55, 22 June 2011 (UTC)

Clarity - simpler point of view

Am I correct in saying that a density on a manifold is just the absolute value of a top degree form? If so, why make it so complicated? 130.149.76.169 (talk) 12:45, 11 January 2017 (UTC)