{"id":44,"date":"2015-10-23T15:56:39","date_gmt":"2015-10-23T15:56:39","guid":{"rendered":"http:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/?p=44"},"modified":"2015-10-23T15:56:39","modified_gmt":"2015-10-23T15:56:39","slug":"assignment-6","status":"publish","type":"post","link":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/2015\/10\/23\/assignment-6\/","title":{"rendered":"Assignment 6"},"content":{"rendered":"<p>Due Friday, October 30<\/p>\n<p>3.2.3, 3.3.5 through 3.3.8, From Section 3.11: #11, 12, 22<\/p>\n<p>A. If \\(f:(X,x) \\to (Y,y)\\) is a continuous map of pointed topological spaces, verify that \\(f_\\ast: \\pi_1(X,x) \\to \\pi_1(Y,y)\\) is a group homomorphism. I showed you the steps in class. Justify them.<\/p>\n<p>B. If \\(f:(X,x) \\to (Y,y)\\) and \\(g:(Y,y) \\to (Z,z)\\), verify that \\(g_\\ast \\circ f_\\ast = (g\\circ f)_\\ast\\).<\/p>\n<p>C. If \\(f:(X,x) \\to (X,x)\\) is the identity map, prove \\(f_\\ast\\) is the identity map on the fundamental group.<\/p>\n<p>I will select some problems from those to grade. Please ask me about any questions you have on the problems that are not graded.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Due Friday, October 30 3.2.3, 3.3.5 through 3.3.8, From Section 3.11: #11, 12, 22 A. If \\(f:(X,x) \\to (Y,y)\\) is a continuous map of pointed topological spaces, verify that \\(f_\\ast: \\pi_1(X,x) \\to \\pi_1(Y,y)\\) is a group homomorphism. I showed you the steps in class. Justify them. B. If \\(f:(X,x) \\to (Y,y)\\) and \\(g:(Y,y) \\to (Z,z)\\), [&hellip;]<\/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\/fall2015mat661\/wp-json\/wp\/v2\/posts\/44"}],"collection":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/comments?post=44"}],"version-history":[{"count":4,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/posts\/44\/revisions"}],"predecessor-version":[{"id":48,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/posts\/44\/revisions\/48"}],"wp:attachment":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/media?parent=44"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/categories?post=44"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/fall2015mat661\/wp-json\/wp\/v2\/tags?post=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}