Due Friday, October 9

Exercises 2.9.25 to 2.9.33.

Be sure and give all the details. For example, I might say, “You can check that…” But on your homework, you can’t say that. You have to check that…

The author’s hint on #26 might be confusing. Here’s a simpler version: think polar coordinates. Any point in \(D^2\) is \(r e^{i\theta}\) where \(r\) between 0 and 1. The “coning” refers to the fact that all of the angles \(\theta\) determine the same point if \(r=0\). This is a certain type of quotient space called the cone: for a space \(X\), the cone is \(CX := X\times[0,1] / (x\times 0 \sim y\times 0:\ x,y\in X)\). The disc is the cone of a circle, up to homeomorphism. The author is asking (more or less), for you to extend an isotopy of the homeomorphism of the circle to an isotopy over the disc by using the \(r\) parameter to shrink inwards.

I will select some problems from those to grade. Please ask me about any questions you have on the problems that are not graded.