2
$\begingroup$

I read that an oriented manifold is a manifold with a choice of orientations for each tangent space so that for $p \in M$, there is an open set $U$ and a collection of vector fields $X_1,...,X_n$ so that for all $q \in U$ $X_1(q),...,X_n(q)$, is a basis of $T_qM$ belonging to the orientation of $T_qM$. What does it mean for manifold to be "orientable"? Is it the same thing as oriented?

  • 0
    Two related answers (full disclosure: by me) http://math.stackexchange.com/questions/146585/a-question-about-orientation-on-a-manifold/146599#146599, http://math.stackexchange.com/questions/131130/orientation-on-mathbbcp2/2012-12-06

3 Answers 3