{"id":192,"date":"2013-04-17T20:17:03","date_gmt":"2013-04-17T20:17:03","guid":{"rendered":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/?p=192"},"modified":"2013-07-16T13:33:14","modified_gmt":"2013-07-16T13:33:14","slug":"homework-13","status":"publish","type":"post","link":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/2013\/04\/17\/homework-13\/","title":{"rendered":"Homework 13"},"content":{"rendered":"<p>Due Thursday, April 25, in class.<\/p>\n<p>A. Prove the splitting lemma.<\/p>\n<p>p. 176, Hatcher<\/p>\n<p># 1, 2, 8<\/p>\n<p>Extra hint for 2: it is easy to get confused about the subscripts.  Recall that a connected graph has (reduced) nonzero homology only in dimension one.  This observation will save you a lot of trouble when considering Mayer-Vietoris sequences.  Once you have figured out the case where \\(X\\) is a tree, build up to arbitrary graphs by adding edges one at a time.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Due Thursday, April 25, in class. A. Prove the splitting lemma. p. 176, Hatcher # 1, 2, 8 Extra hint for 2: it is easy to get confused about the subscripts. Recall that a connected graph has (reduced) nonzero homology only in dimension one. This observation will save you a lot of trouble when considering [&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\/192"}],"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=192"}],"version-history":[{"count":2,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/posts\/192\/revisions"}],"predecessor-version":[{"id":195,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/posts\/192\/revisions\/195"}],"wp:attachment":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/media?parent=192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/categories?post=192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2013mat761\/wp-json\/wp\/v2\/tags?post=192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}