Turn in 3 problems from the ones below<\/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, April 22.<\/p>\n
p 155 # 21
\np 165 # 1, 4<\/p>\n
A. Find a CW complex structure for the Klein bottle cross the circle. Compute homology. Compare to Klein bottle’s homology. Think about the example in class of various dimensional tori. Formulate a guess for what is the homology of \\(X \\times S^1\\) in terms of the homology of \\(X\\).<\/p>\n
B. Consider a space \\(X\\) and the space \\(X \\times S^1\\). Compute the homology groups of \\(X\\times S^1\\) in terms of the homology groups of \\(X\\) using Mayer-Vietoris.<\/p>\n
C. Did you do E last week? If so, consider \\(\\mathbb{R}^3 – K \\subset S^3 – K \\). Using a Mayer-Vietoris sequence, find a generator for \\(H_2(\\mathbb{R}^3-K)\\).<\/p>\n","protected":false},"excerpt":{"rendered":"
Turn in 3 problems from the ones below 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. Due Wednesday, April 22. p 155 # […]<\/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\/101"}],"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=101"}],"version-history":[{"count":2,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/posts\/101\/revisions"}],"predecessor-version":[{"id":103,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/posts\/101\/revisions\/103"}],"wp:attachment":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/media?parent=101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/categories?post=101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2015mat761\/wp-json\/wp\/v2\/tags?post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}