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Assigned Thursday January 20; due Thursday February 3, 3PM, in class

this document in PDF: HW.pdf

**Required 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! An excellent idea is to re-read Hatcher's section 1.3 with a very
active perspective. Which of his theorems are corollaries of our ``main
theorem of coverings''? Which of his theorems are lemmas used in the
proof of the ``main theorem of coverings''? Also, read Hatcher's pages
97-128.

**Solve the following problems. ** (But submit
only the odd-numbered ones). In Hatcher's book, problems 11-18 on page
132.

**Just for fun. ** A maximal tree is chosen within
the edges of the integer lattice. Show that there are two
neigboring points on the lattice whose distance from each other,
measured only along the tree, is at least .

A maximal tree in the integer lattice

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Dror Bar-Natan 2005-01-20