{"id":167,"date":"2013-03-28T17:27:23","date_gmt":"2013-03-28T17:27:23","guid":{"rendered":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/?p=167"},"modified":"2013-07-16T13:33:15","modified_gmt":"2013-07-16T13:33:15","slug":"homework-10","status":"publish","type":"post","link":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/2013\/03\/28\/homework-10\/","title":{"rendered":"Homework 10"},"content":{"rendered":"<p>Hatcher p 155<\/p>\n<p># 3, 4, 8, 9c, 12, 27.<\/p>\n<p>On 9c, describe geometrically the generators of the homology groups.<\/p>\n<p>On 8, follow this hint if you wish: first show that \\(\\widehat{f}: S^2 \\to S^2 \\) is homotopic to \\(z^{\\mathrm{deg\\ } f}\\) where \\( f(z):\\mathbb{C}\\to\\mathbb{C} \\) is the polynomial you are given.  Then there is only one thing to show on this problem.  Why?<\/p>\n<p>Read Example 2.31 p 136, and Exercise 1 p 155.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hatcher p 155 # 3, 4, 8, 9c, 12, 27. On 9c, describe geometrically the generators of the homology groups. On 8, follow this hint if you wish: first show that \\(\\widehat{f}: S^2 \\to S^2 \\) is homotopic to \\(z^{\\mathrm{deg\\ } f}\\) where \\( f(z):\\mathbb{C}\\to\\mathbb{C} \\) is the polynomial you are given. Then there is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/posts\/167"}],"collection":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/comments?post=167"}],"version-history":[{"count":5,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/posts\/167\/revisions"}],"predecessor-version":[{"id":198,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/posts\/167\/revisions\/198"}],"wp:attachment":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/media?parent=167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/categories?post=167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/tags?post=167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}