MATH6071A  Topics in Topology I  2015/16
Announcement
 There is no class on Sept 8 (Sept 7's lecture had extra 45mins)
General Information
Lecturer

YiJen LEE
 Office: AB1 412
 Email:
Time and Venue
 Lecture: Mondays 7:309:00 pm; Tuesdays 4:455:30pm at AB1 502a
Course Description
Selected topics in low dimensional topology.
References
 SchultensIntroduction to 3manifolds
 Casson & BleilerCasson & BleilerAutomorphisms of surfaces after Nielsen and Thurston
 BuoncristianoFragments of geometric topology from the sixties, part I. (http://www.emis.de/journals/GT/gtmcontents6.html)
 Hempel3manifolds
 RolfsenKnot and Links
 GordonLectures on normal surface theory. (https://www.math.wisc.edu/~rkent/normal.pdf)
 LackenbyLectures on 3manifolds. (https://homepages.warwick.ac.uk/~masgar/Articles/Lackenby/thrmn812.pdf)
 JacoLectures on 3manifold topology.
 HatcherNotes on basic 3manifold topology. (https://www.math.cornell.edu/~hatcher/3M/3M.pdf)
 Aschenbrenner & Friedel & Wilton3manifold groups
 Jenkins & NeumannLecture notes on Seifert manifolds
 CaligariNotes on 3manifolds (http://math.uchicago.edu/~dannyc/courses/3manifolds_2014/3_manifolds_notes.pdf)
 ThurstonUnpublished lecture notes (http://library.msri.org/books/gt3m/PDF/1.pdf)
Preclass Notes
 W1 &2: Buoncristiano; Schultens Ch.1
 W3: Buoncristiano; Schultens Ch. 3.
 W4 &5: Schultens Ch.3 &5; Rolfsen Ch. 9B; Hempel Ch. 13.
 W68: Schultens Ch.3&5; Gordon's and Lackenby's notes.
 W8: Jaco Ch.6.
 W10: Hatcher Section 1.2.
 W11& 12: JankinsNeumann;
 W13: AschenbrennerFriedelWilton Ch. 1; Caligari Ch.5; Thurston Ch.4; Casson & Biler
Lecture Notes
 Week 1& 2: the three categories of manifolds (TOP, PL, DIFF); summary and current status of essential basic results/conjectues.
 Week 3: (TOP/PL/DIFF) R^n and S^n; their automorphisms. Connected sums. Knot equivalences and isotopy extension theorems. (3manifolds): Prime decomposition, Irreducible manifolds, essential surfaces, The sphere theorem.
 Week 4& 5: Dehn's Lemma; loop theorem; Papakyriakopoulos's tower construction; criterion for existence of incompressible surfaces; Hierarchies and Haken's theorem; Waldhausen's theorem; 3manifolds that are homotopic but not homeomorphic; Lens spaces.
 Week 6: Whitehead manifolds; normal surface theory.
 Week 7: Haken finiteness; Diophantine equalities. "Topological rigidity" for surfaces.
 Week 8: Topological rigidity for Haken manifolds; Algorithm to detect the unknot; Seifert fibered spaces;
 Week 9: East Asian Symplectic Conference
 Week 10: Surfaces in Seifert fibered spaces; the JSJ decomposition.
 Week 11: Seifert invariants, uniqueness of SFS structures; SFS and \pi_1; Brieskorn spheres; manifolds;
 Week 12: "Geometrization" of 2d orbifolds and SFS
 Week 13: Torus theorem and Seifert fibered theorem; Thurston's geometrization of 3manifolds; Sol and Nil manifolds; Thurston's classification of surface automorphism and geometry of mapping tori; examples of hyperbolic and nonHaken manifolds from knot surgery
Assignments
Last updated: December 02, 2015 14:43:02