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--- blog:2023-06-18 [2023/06/19 05:37] – [Teleman's shift] pzhou
+++ blog:2023-06-18 [2023/06/25 15:53] (current) – external edit 127.0.0.1
@@ Line 25: / Line 25: @@
 Then, we need to consider homology of the space. We cannot just handwave, otherwise it is the same as saying 'path-integral'.
-What does homology mean? The Schubert cell is a nice cell. Given
+What does homology mean? The Schubert cell is a nice cell. Given a cocharacter $\C^* \to G$, means given an element in $G(K)$. We may consider the $G(O)-G(O)$ double coset. That might be what we mean when we say $G(O)$-equivariant cohomology. I guess, we can do $G(O)$-conjugation action's equivariance. Then, it would be compatible with composition.
+What's the most naive thing? just do set, and union. pointwise operation, take the image of the map.
+Then, what does monopole operator mean? And what does a BM equivariant homology cycle mean? What does equivariant mean? If we consider $S^2$ mod $U(1)$, what do we get? I would take the Borel construction.
+Let's blackbox a bit. BFN and Teleman deals with matter differently. In BFN, we use the same indexing set for basis. The multiplication rule for the 'monopole' operators are different. The monopole operators are the global coordinate, the global fiber coordinates. If you compose two fundamental cycle of Schubert varieties, you can get a lot of stuff. When you encounter folding, in the sense that two input arrows