© | Dror Bar-Natan: Talks: LesDiablerets-1508: < >

# Kuno's Talk 1

 width: 400 720 1280 orig/LD15_Kuno-1.avi For now, this video can only be viewed with web browsers that support

Notes on LD15_Kuno-1:    [edit, refresh]

refresh
panel
Managed by dbnvp: The small-font numbers on the top left of the videos indicate the available native resolutions. Click to test.

0:05:35  The mapping class group and $\pi_1$.
0:09:25  The Johnson filtration.
0:12:50  The Johnson filtration, 2.
0:14:50  The Johnson homomorphism. In the Artin case, this is the action of the Drinfel'd-Kohno Lie algebra on the free Lie algebra.
0:19:35  A geometric construction.
0:22:55  This seems to be the theorem on page 7 of Kawazumi's notes. The completion $\widehat{{\mathbb Q}\pi}$ is relative to powers $(I\pi)^p$ of the augmentation ideal. The completion $\widehat{{\mathbb Q}\hat\pi}$ is relative to ${\mathbb Q}{\mathbb 1}+|(I\pi)^p|$.
0:23:18  According to page 8 of Kawazumi's notes, $\tau$ is related to the Massuyeau Johnson map.
0:25:34  $\tau$ and simple closed curves.
0:31:06  $\tau(t_C) = L(C) = \left|\frac12(\log x)^2\right|$
0:34:32  Proof of $\tau(t_C) = L(C) = \left|\frac12(\log x)^2\right|$.
0:38:03  Generalized Dehn twists.
0:42:52  Given a symplectic expansion $\theta$...
0:48:00  $\delta\circ\tau=0$.
0:50:55  $\delta\circ\tau=0$, part II. What's the geometry behind this?
0:54:46  $\delta^{alg}$.
0:57:52  Is there $\theta$ such that $\delta^\theta=\delta^{alg}$?