40740 - Topology (Fall 2019)
Course Info
Who: Daniel Studenmund
What: Math 40740 - Topology
When: 12:50-1:40 MWF
Where: DeBartolo 216
Why: TBD
Office: Hurley 166B
Office Hours: Mondays 4-5, Tuesdays 1:30-2:30, Fridays 10:30-12:00, and by appointment
Syllabus: [pdf]
Homework
Homework 10, due 12/11: Section 9.1, exercises 5, 8, Section 9.2 exercises 1, 4a, 4b (Caution: there is a typo in problem 5. It should refer to 9.1.8, not 9.1.5.)
Homework 9, due 11/25: Section 9.1, exercises 2, 3bd, 6, 7, 11 (For exercise 3, you need not carefully justify continuity of your homotopies. For exercises 6, 7, and 11, just give an intuitive explanation of your answer, rather than a full rigorous proof)
Homework 8, due 11/13: Section 5.4, exercises 2ac, 3a, 9
Homework 7, due 11/6: [pdf link]
Homework 6, due 10/9: Section 3.1 exercise 6, and Section 3.2 exercises 1de, 2de, 8
Homework 5, due 10/2: [pdf link]
Homework 4, due 9/25: [pdf link]
Homework 3, due 9/18: [pdf link]
Homework 2, due 9/11: Section 10.1 exercises 3, 5, 8, 14, Section 10.2 exercise 10
Homework 1, due 9/4: Section 1.1, exercises 1-4
Notes
Day 39 (12/6) -- Surface group presentations and the word problem
Day 38 (12/4) -- Fundamental group of surfaces (part two)
Day 37 (12/2) -- Fundamental group of surfaces (part one)
Day 36 (11/25) -- Plane with punctures, free groups, homeomorphism invariance
Day 35 (11/22) -- Fundamental group of a plane with puncture(s)
Day 34 (11/20) -- The fundamental group
Day 33 (11/18) -- Homotopy and path operations
Day 32 (11/15) -- Winding number
Day 30 (11/11) -- Jones polynomial: transformations
Day 29 (11/8) -- Jones polynomial: isotopy invariance
Day 28 (11/6) -- Jones polynomial: definition
Day 27 (11/4) -- Jones polynomial: computations
Day 26 (11/1) -- Intrinsic linking and embeddability
Day 25 (10/30) -- Linking number
Day 24 (10/28) -- Link splittings and labelability
Day 23 (10/18) -- Reidemeister moves and p-labeling
Day 22 (10/16) -- Knots and isotopy
Day 21 (10/14) -- Surfaces wrap-up
Day 20 (10/11) -- Proof of classification of surfaces
Day 19 (10/9) -- Cut-and-paste transformations
Day 18 (10/7) -- Building surfaces
Day 17 (10/4) -- Orientability and Euler characteristic
Day 16 (10/2) -- Surfaces (different presentations of the torus)
Day 15 (9/30) -- Surfaces (continued)
Day 13 (9/25) -- Planarity and coloring
Day 12 (9/23) -- Adjacency matrices and Euler's formula
Day 11 (9/20) -- Graph homeomorphism
Day 9 (9/16) -- Compactness and covers
Day 8 (9/13) -- Connectedness, continued
Day 6 (9/9) -- Topological spaces, continued
Day 5 (9/6) -- Topological spaces
Day 4 (9/4) -- Open subsets of metric spaces