Outward-normal-first boundary orientation
= Outward-normal-first boundary orientation
The boundary of an oriented manifold with boundary is oriented by the outward-normal-first convention: an ordered basis $(v_2,\ldots,v_n)$ of $T_p\partial X$ is positive when $(v_1,v_2,\ldots,v_n)$ is positive in $T_pX$ for an outward-pointing normal $v_1$.