MATH 215C Spring 2017

Course Information



Lectures: MWF 12:10 in 108 Hoagland.
Text: Algebraic Topology by Allen Hatcher.
Syllabus: Department Syllabus.

Course Outline: The course will briefly cover homology, cohomology and Poincare duality from chapters 2 and 3 followed by obstruction theory and possibly other topics from chapter 4. Obstruction theory will follow Chapter 7 of Davis and Kirk.

This is a rough and optimistic outline of when topics will be covered and will be edited as the term progresses. The exam scheduling will not change. Homework problems will also be added with assignments collected on Friday s.

DayDateSection(#s) coveredHomework
MondayApril 32.2: Degree
WednesdayApril 52.2: vector field and local homology
FridayApril 72.2: Moore spaces
MondayApril 102.2: lens spaces, 2B: transfer
WednesdayApril 122B: Borsuk-Ulam, 2.2: deg(rational), 2C: Lefschetz
FridayApril 14 2.2.3, 2.2.8, 2.2.32(or 2.1.20), 2B.11, 2C.4. Feel free to turn in Monday April 17.
MondayApril 172.2: Axioms and Mayer-Vietoris
WednesdayApril 194.3: Axioms and Uniqueness
FridayApril 214.3: Axioms and Uniqueness
MondayApril 243.1: Cohomology
WednesdayApril 263.2: Cup Product
FridayApril 283.2: Kunneth and gr-commutative
MondayMay 1MidtermFigure
WednesdayMay 33.3: Poincare Duality
FridayMay 53.3 PD: Semisimplicial sets
MondayMay 83.3 PD: Subdivision3.1.4, 3.1.7, 3.2.1, 3.2.3, 3.2.4, 3.2.11, 3.2.14, 3.2.18, Midterm. Feel free to turn in Monday.
WednesdayMay 103.3 PD: Dual Cells
FridayMay 123.3 PD: Compact Support, AD
MondayMay 153.3: Cup and Cap Products
WednesdayMay 174.3 Obstruction Theory
FridayMay 19Davis 7.1: Obstruction Problem
MondayMay 22Davis 7.3: Obstruction Class 3.3.6, 3.3.7, 3.3.11, 3.3.16, 3.3.20, 3.3.21, 3.3.26, 3.3.32.
WednesdayMay 24Davis 7.5: Homotopy Obstruction
FridayMay 26Davis 7.7: Cohomology from K(g,n)
MondayMay 29 no class
WednesdayMay 314.3: Loop Spectra Davis: 117, 118, 119, 4.1.12, 4.1.18, 4.3.24.
FridayJune 2Davis 7.10: Lifting Obstructions
MondayJune 5Davis 7.11: Characteristic Classes
WednesdayJune 7 final