————————————————————-<\/p>\n
Algebraic and Geometric Topology. Part 1<\/b>
\n1\u00a0 Extension and lifting problems<\/p>\n
1.1\u00a0 The language of homotopy theory
\n1.2\u00a0 The identity map extension problem
\n1.3\u00a0 The identity map lifting problem<\/p>\n
2\u00a0 Fundamental groups and coverings<\/p>\n
2.1\u00a0 Paths, loops, and the fundamental group
\n2.2\u00a0 Coverings and their automorphism groups
\n2.3\u00a0 Cayley graphs and complexes<\/p>\n
3\u00a0 Manifolds and Lie groups<\/p>\n
3.1\u00a0 Spheres and projective spaces
\n3.3\u00a0 Classical matrix groups
\n3.3\u00a0 Spheres as H-spaces<\/p>\n
4\u00a0 Low dimensional manifolds<\/p>\n
4.1\u00a0 Classification of 1-manifolds
\n4.2\u00a0 Classification of 2-manifolds
\n4.3\u00a0 The Poincare 3-sphere<\/p>\n
5\u00a0 Knots, links, and braids<\/p>\n
5.1\u00a0 The genus of a knot
\n5.2\u00a0 The linking number
\n5.3\u00a0 The braid groups<\/p>\n
———————————————————-
\nAlgebraic and Geometric Topology. Part 2
\n<\/b>
\n1\u00a0 Homology and cohomology groups<\/p>\n
1.1\u00a0 Homology groups – singular and cellular
\n1.2\u00a0 Cohomology groups and rings
\n1.3\u00a0 Poincare duality for manifolds<\/p>\n
2\u00a0 Homotopy groups and fibrations<\/p>\n
2.1\u00a0 The Hurewicz theorem
\n2.2\u00a0 The Whitehead theorem
\n2.3\u00a0 The exact sequence of fibration<\/p>\n
3\u00a0 Homotopy theory<\/p>\n
2.1\u00a0 Aspherical CW complexes
\n2.1\u00a0 Eilenberg-McLane spaces
\n2.3\u00a0 Postnikov systems<\/p>\n
4\u00a0 Four and higher dimensional manifolds<\/p>\n
3.1\u00a0 Simply connected four manifolds
\n3.2\u00a0 Fundamental groups of homology spheres
\n3.3\u00a0 The h-cobordism and s-cobordism theorems<\/p>\n
5\u00a0 Smooth manifolds and vector fields<\/p>\n
5.1\u00a0 Intersection numbers and transversality
\n5.2\u00a0 Lefschetz fixed point theory
\n5.3\u00a0 The Poincare-Hopf Theorem<\/p>\n
———————————————————-
\nAlgebraic and Geometric Topology. Part 3
\n<\/b><\/p>\n
1. Vector bundles<\/p>\n
2. Characteristic classes<\/p>\n
3. Topological K<\/i>-theory<\/p>\n
4. Cobordism theory<\/p>\n
5. Manifolds and modular forms
\n——————————————————-<\/p>\n","protected":false},"excerpt":{"rendered":"
————————————————————- Algebraic and Geometric Topology. Part 1 1\u00a0 Extension and lifting problems 1.1\u00a0 The language of homotopy theory 1.2\u00a0 The identity map extension problem 1.3\u00a0 The identity map lifting problem 2\u00a0 Fundamental groups and coverings 2.1\u00a0 Paths, loops, and the fundamental group 2.2\u00a0 Coverings and their automorphism groups 2.3\u00a0 Cayley ( more… )<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"kt_blocks_editor_width":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=\/wp\/v2\/posts\/172"}],"collection":[{"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=172"}],"version-history":[{"count":3,"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=\/wp\/v2\/posts\/172\/revisions"}],"predecessor-version":[{"id":175,"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=\/wp\/v2\/posts\/172\/revisions\/175"}],"wp:attachment":[{"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kpa.faculty.wmi.amu.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}