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--- blog:2023-05-01-signs [2023/05/01 06:34] – created pzhou
+++ blog:2023-05-01-signs [2023/06/25 15:53] (current) – external edit 127.0.0.1
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 I need to worry about signs. This is done in Seidel's book, thank goodness. At least I know if I try hard enough, I can understand it.
+===== section 11 of Seidel =====
+What is orientation? it is not a framing, but just an element in the top exterior power of the tangent space. Or, equivalently, top ext of the cotangent space.
+In Morse theory, suppose we have a downward gradient flow from $p$ to $q$, of index $1$, then, if we insert the downward flow tangent vector into the top ext form of negative eigenspace at $p$, we get the negative eigenspace at $q$.
+In Floer theory, the downward flowing manifold has too high a dimension. What does the orientation space of an intersection mean? And how does $A_\infty$ operations relates them?