An anchor is the bundle map 
from a vector bundle 
to the tangent
bundle TB satisfying
1. ![[rho(X),rho(Y)]=rho([X,Y])](/images/equations/Anchor/Inline3.svg)
and
2. ![[X,phiY]=phi[X,Y]+(rho(X)·phi)Y,](/images/equations/Anchor/Inline4.svg)
where 
and 
are smooth sections of 
, 
is a smooth function of 
,
and the bracket is the "Jacobi-Lie bracket" of a vector
field.
Anchor
See also
Bundle, Lie AlgebroidExplore with Wolfram|Alpha
References
Weinstein, A. "Groupoids: Unifying Internal and External Symmetry." Not. Amer. Math. Soc. 43, 744-752, 1996.Referenced on Wolfram|Alpha
AnchorCite this as:
Weisstein, Eric W. "Anchor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Anchor.html