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--- math214:final-solution [2020/05/17 16:17]
pzhou created
+++ math214:final-solution [2020/05/17 16:23] (current)
pzhou [Problem 7]
@@ Line 116: / Line 116: @@
 The form  $\omega_3$  on  $GL(\R^N)$  can be defined as following
  $\omega_3 := tr( g^{-1} dg \wedge g^{-1} dg \wedge g^{-1} dg).$
+------
+Some of you tried to construct a linear interpolation of connections  $\nabla_t = t \nabla^L + (1-t) \nabla^R$ , and find that it is not flat for  $t \in (0,1)$ . That is only circusmstancial evidence that there are no path //within flat connections// between  $\nabla^L$  and  $\nabla^R$ , but not a proof.
 ==== Afterwords ====

Lecture Notes