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--- blog:2023-06-15 [2023/06/16 17:46] – [add matter: the original definition] pzhou
+++ blog:2023-06-15 [2023/06/25 15:53] (current) – external edit 127.0.0.1
@@ Line 46: / Line 46: @@
 ==== add matter: the original definition ====
-We follow BFN, and build the linear bundle $L_V$ over the algebraic model of loop to $G$, which is like the free loop quotient by equivalence $Gr_G = G((z) )/ G[[z ] ]$. Given a Laurent loop $\gamma \in G((z) )$, we can look for those $\gamma$-robust pairs, namely those nice global section of $V$ over the disk $D$, such that, even if we do a singular gauge transformation / multiply by the section to the group, we are still holomorphic. This $\gamma$ really looks like a transition function of a principal $G$ bundle on a raviolo $B$, and we take the associated $V$-bundle, and then $L_V|_\gamma$ by definition is the global section, $\Gamma(B, V_\gamma)$.
+We follow BFN, and build the linear bundle $L_V$ over the algebraic model of loop to $G$, which is like the free loop quotient by equivalence $Gr_G = G((z) )/ G[ [z ] ]$. Given a Laurent loop $\gamma \in G((z) )$, we can look for those $\gamma$-robust pairs, namely those nice global section of $V$ over the disk $D$, such that, even if we do a singular gauge transformation / multiply by the section to the group, we are still holomorphic. This $\gamma$ really looks like a transition function of a principal $G$ bundle on a raviolo $B$, and we take the associated $V$-bundle, and then $L_V|_\gamma$ by definition is the global section, $\Gamma(B, V_\gamma)$.