0708-1300/Homework Assignment 12

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Errata to Bredon's Book

In Preparation

The information below is preliminary and cannot be trusted! (v)

Reading

Read, reread and rereread your notes to this point, and make sure that you really, really really, really really really understand everything in them. Do the same every week!

Also, read section 8-11, 13 and 18-20 of chapter IV of Bredon's book three times:

First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.

Doing

Solve all the problems in pages 206-207 of Bredon's book, but submit only your solutions of problems 1, 5, 9, and all the problems in pages 230 but submit only problem 1.

Also, solve and submit the following:

Problem. Given a CW-space $K$ with $n$ -cells indexed by $K_{n}$ and skeleta denoted $K^{n}$ , show that the map $\partial _{1}:\langle K_{n}\rangle \to \langle K_{n-1}\rangle$ given by the composition $H_{n}(K^{n},K^{n-1})\longrightarrow H_{n-1}(K^{n-1})\longrightarrow H_{n-1}(K^{n-1},K^{n-2})$ is equal to the one defined using degrees: $\partial _{2}\sigma =\sum _{\tau \in K_{n-1}}[\tau :\sigma ]\tau$ , where $[\tau :\sigma ]:=\deg p_{\tau }\circ f_{\partial \sigma }$ and the $f_{\partial \sigma }$ 's are the gluing maps defining $K$ .