blog:2023-05-01-signs
2023-05-01 signs
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?
blog/2023-05-01-signs.txt · Last modified: 2023/06/25 15:53 by 127.0.0.1