direct image

If $f:X\to Y$ is a continuous map of topological spaces and $\mathcal{F}$ is a sheaf on $X$, the direct image sheaf, $f_{*}\mathcal{F}$ on $Y$ is defined by

$(f_{*}\mathcal{F})(V)=\mathcal{F}(f^{-1}(V))$

for open sets $V\subset Y$, with the restriction maps induced from those of $\mathcal{F}$.

Title direct image DirectImage1 2013-03-22 12:03:10 2013-03-22 12:03:10 nerdy2 (62) nerdy2 (62) 8 nerdy2 (62) Definition msc 54B40