In Allen Hatcher's Algebraic Topology, $X\vee Y$ means the "wedge sum" of two (topological) spaces $X$ and $Y$. However, in $\LaTeX$, \wedge is the notation for $\wedge$, while $\vee$ is wirtten \vee. Where does this inconsistency come from?
[Math] What does “wedge” mean
notation
Best Answer
The inconsistency comes from different mathematicians doing different branches of mathematics.
In exterior algebra, a wedge product is written with an upward-pointing wedge, like this: $\alpha \wedge \beta.$
The wedge sum in topology is written with a downward-pointing wedge.
Only one of those symbols can be called
\wedgein LaTeX. Evidently the terminology from exterior algebra won in this case.