Syllabus
Course Description
In this course we will survey various aspects of 3-manifolds including: 2-dimensional orbifolds, Seifert fibered spaces, Thurston's 8 geometries, separability properties, Haken manifolds, and other items as time permits (Virtually Fibered Theorem, Virtual Haken Theorem, decompositions of 3-manifolds, etc.)
Resources
Martelli's text An Introduction to Geometric Topology
Hatcher's text Basic 3-Manifold Topology
Notes on hyperbolic 2-space
Notes on hyperbolic 3-space
Hatcher's text Basic 3-Manifold Topology
Notes on hyperbolic 2-space
Notes on hyperbolic 3-space
Course Notes
Jan 10
Jan 12
Jan 17
Jan 19 (I only got through the proof of Prop 9.2.14)
Reading Assignment for week of Jan 23: this only works if you actually do the reading!! feel free to work together
Martelli's book Sections 9.2.6, 9.2.7 (you will need to read Sec 1.7.5 for this and you can skip exercise 9.2.22), 9.2.8 and 9.2.9 (you can skim the proofs in these two sections, but you need the statements of results for the next section), and finally Section 9.2.10 (this is the really important proof that I want you to go through carefully).
Feb 7 (together we skimmed 9.2.11, 9.2.12, & 9.2.13 before covering what is in the notes in more detail)
Feb 9
Feb 14
Feb 16/18/21 Reading Assignment: Lemma 9.4.6 & Sections 9.4.2, 9.4.3, 9.4.4, 9.4.5, 9.4.6
Feb 23
Feb 28
Mar 2
Mar 16
Mar 21
Mar 23
Mar 28 & conference talk notes
Mar 30
Apr 4
Apr 6
Apr 11
Apr 18
Apr 20: class reading & discussion-- Ch 4 up until Section 4.2.4 (will start at this section next time and finish our discussion of the thick-thin decomposition)
Apr 25
Jan 12
Jan 17
Jan 19 (I only got through the proof of Prop 9.2.14)
Reading Assignment for week of Jan 23: this only works if you actually do the reading!! feel free to work together
Martelli's book Sections 9.2.6, 9.2.7 (you will need to read Sec 1.7.5 for this and you can skip exercise 9.2.22), 9.2.8 and 9.2.9 (you can skim the proofs in these two sections, but you need the statements of results for the next section), and finally Section 9.2.10 (this is the really important proof that I want you to go through carefully).
Feb 7 (together we skimmed 9.2.11, 9.2.12, & 9.2.13 before covering what is in the notes in more detail)
Feb 9
Feb 14
Feb 16/18/21 Reading Assignment: Lemma 9.4.6 & Sections 9.4.2, 9.4.3, 9.4.4, 9.4.5, 9.4.6
Feb 23
Feb 28
Mar 2
Mar 16
Mar 21
Mar 23
Mar 28 & conference talk notes
Mar 30
Apr 4
Apr 6
Apr 11
Apr 18
Apr 20: class reading & discussion-- Ch 4 up until Section 4.2.4 (will start at this section next time and finish our discussion of the thick-thin decomposition)
Apr 25