## Fall 2018

### December

#### 10

You can retrieve the last homework paper at my office door. The course grades have been uploaded and should be available soon. Enjoy your winter break!

Recommended viewing for the Christmas season: John Milnor's 1965 Hedrick lectures on differential topology at Cornell.

#### 02

Last homework updated (explanation for problem 5 added). Last office hours today at 2:00 pm.

Deadline for last homework has been extended to Tuesday 4 December at 5:00 pm.

### November

#### 18

Last homework posted. 20 and 27 November office hours cancelled. Last office hours TBA.

#### 13

New due date for homework 10 is Friday 16 Nov 5:00 pm.

Hint for problem 3(c) (typo corrected). Let $J\subseteq I$ be the maximal existence interval for the solution $\zeta$. So we have $\zeta\colon J\to G$, $t_0\in J$, $\zeta(t_0)=g_0$ and $\zeta'(t)=\delta_G(t,\zeta(t))$ for $t\in J$. Suppose that $J$ is a proper subinterval of $I$. Then either (1) $\tau=\sup(J)<\sup(I)$ or (2) $\inf(J)>\inf(I)$. Let's consider case (1). The initial value problem for $\delta_R$ with initial value $1\in G$ and starting time $\tau$ has a solution $\eta\colon J_\tau\to G$, where $J_\tau$ is an open interval containing $\tau$. Choose $t_1\in J\cap J_\tau$ and let $g_1=\eta(t_1)^{-1}\zeta(t_1)$. For $t\in J_\tau$ let $\chi(t)=\eta(t)g_1$. What can you say about the path $\chi\colon J_\tau\to G$?

#### 09

Office hours Tuesday 13 Nov will be 3:00 pm–4:30 pm.

#### 08

Tenth homework posted.

### October

#### 31

Ninth homework posted.

#### 24

Eighth homework amended.

#### 24

Eighth homework posted.

#### 17

Seventh homework posted; due Wednesday 24 October.

#### 05

Sixth homework posted; due Wednesday 17 October.

### September

#### 28

Fifth homework posted; due Friday 5 October.

#### 24

Deadline fourth homework extended to Friday 28 September.

#### 12

Fourth homework posted.

#### 12

Third homework posted.

#### 05

Second homework posted.

### August

#### 22

Announcements for Math 6520 will be posted on this home page. Course information can be found through the links at the top. Please familiarize yourself with the general information on the Info page.

The first homework has been posted and is due on the Wednesday after Labor Day.