{"id":3397,"date":"2022-05-02T13:29:08","date_gmt":"2022-05-02T17:29:08","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=3397"},"modified":"2026-03-19T08:10:30","modified_gmt":"2026-03-19T12:10:30","slug":"first-year-topology-exam-ii-materials","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/first-year-topology-exam-ii-materials\/","title":{"rendered":"First Year Topology Exam II Materials"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">First Year Topology Exam II Materials<\/h1>\n\n\n\n<h4 class=\"wp-block-heading\">In general, the material on the exam is everything we covered in the course but does <span style=\"color: #ff0000\">not<\/span> include the TDA material we did at the end. So it does <span style=\"color: #ff0000\">not<\/span> include functors and pushouts, simplicial complexes and homology and the VR and Reeb complexes<\/h4>\n\n\n\n<h4 class=\"wp-block-heading\">These\u00a0 homeworks, review problems and exams will give you some idea of the kind of problems to expect. The problems on TDA which are not on the exam are crossed off in the relevant documents.<\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3398\">tophw2.1<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3399\">tophw2.2<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3400\">tophw2.3<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3401\">tophw2.4<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3402\">tophw2.5<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3403\">toprev2.1<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3404\">toprev2.2<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3405\">topexam2.1<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/boyland\/content-removed\/\" rel=\"attachment wp-att-3406\">topexam2.2<\/a><\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Here is the material covered, Numbers in parentheses are section number from Munkres, <em>Topology<\/em>, 2nd edition. Some sections had just partly covered.<\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>Path homotopy (51)<\/li>\n<li>Fundamental group (52)<\/li>\n<li>Covering spaces (introduction) (53)<\/li>\n<li>Fundamental group of the circle (54)<\/li>\n<li>Retractions and fixed points (55)<\/li>\n<li>Borsuk-Ulam Theorem (57)<\/li>\n<li>Deformation retract and homotopy (58)<\/li>\n<li>Fundamental group of spheres (59)<\/li>\n<li>Fundamental group of sme surfaces<\/li>\n<li>Identification spaces and quotient topology (22)<\/li>\n<li>Algebraic preliminaries to SVK theorem (67-69)<\/li>\n<li>The SVK- push out, classical and generator\/relation versions (70)<\/li>\n<li>Fundamental group of wedge of circles, the torus, the dunce cap, the projective plane (71, 73, 74)<\/li>\n<li>Abelianization of fundamental group (first Homology) (75)<\/li>\n<li>Embeddings of manifolds (36)<\/li>\n<li>Tychonoff Theorem (37)<\/li>\n<li>Stone-<b>\u010cech <\/b>compactification (38)<\/li><\/ul>\n\n\n\n\n\n\n\n\n\n\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-3397","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=3397"}],"version-history":[{"count":4,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3397\/revisions"}],"predecessor-version":[{"id":4090,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3397\/revisions\/4090"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=3397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}