Density bundle
= Density bundle
{title2=$|\Lambda^nT^*M|$}
On an $n$-dimensional <smooth manifold>, the density bundle $|\Lambda^nT^*M|$ is the real <line bundle> whose coordinate transformation uses the absolute value of the <Jacobian determinant>. A density can therefore be integrated without an <orientation of a smooth manifold>. A <Riemannian metric> gives the positive density $\sqrt{\det(g_{ij})}|dx^1\cdots dx^n|$, including on a nonorientable manifold.
// Target: fiber-bundle.bigb