Turn in 3 problems from Section 1.3 and the extra problems (A-D) below, and read Section 1.3<\/p>\n
Disclaimer: You should do all of the suggested problems on your own, and I will assume that you do. I would recommend (for the midterm, final, and qualifying exams) that you do many other problems. I am available for help.<\/p>\n
Due Wednesday, February 11.<\/p>\n
Suggested problems:<\/p>\n
Section 1.3 # 10, 12, 14, 16<\/p>\n
A. Show that the quotient map \\(S^2 \\to \\mathbb{R}P^2\\) is a covering map. This will help on number 14.<\/p>\n
B. Prove this. Let \\(p:\\widetilde{X}\\to X\\) be a covering space. The cardinality \\(\\#p^{-1}(x)\\) of the fiber over a point is locally constant. If \\(X\\) is connected, this is globally constant.<\/p>\n
C. Construct a two-sheeted covering of the Klein bottle by the torus.<\/p>\n","protected":false},"excerpt":{"rendered":"
Turn in 3 problems from Section 1.3 and the extra problems (A-D) below, and read Section 1.3 Disclaimer: You should do all of the suggested problems on your own, and I will assume that you do. I would recommend (for the midterm, final, and qualifying exams) that you do many other problems. I am available […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/posts\/45"}],"collection":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/comments?post=45"}],"version-history":[{"count":3,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/posts\/45\/revisions"}],"predecessor-version":[{"id":48,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/posts\/45\/revisions\/48"}],"wp:attachment":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/media?parent=45"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/categories?post=45"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/tags?post=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}