Topology I

Math 70800 Spring 2017

Tuesday & Thursday , 10:00 am - 11:30 am, Room 6417


Instructor: Abhijit Champanerkar

Office: 4307

Email :

Office Hours: Thursdays 11:30 - 1 pm

Course description

Books
Exams: We will have a final exam at the end of the semester.


Homework

We will have homework every other week. Homeworks will be posted here. Unless otherwise noted, the section numbers and problem numbers refer to the textbook Algebraic Topology by Allen Hatcher.

Week Topic Homework Due
Jan 30 Delta complexes and Simplicial Homology Homework 1 Thursday Feb 16th
Feb 6 Singular homology and Homotopy Invariance (pg 108-113)
Feb 13 Relative Homology (pg 115-118)
Feb 20 Excision and Applications (pg 119-128) Homework 2 Thursday Mar 16th
Feb 27 Mayer-Vietoris Sequence (pg 149-153) & Equivalance (pg 128-131)
Mar 6 Degree and Cellular Homology (pg 134-141)
Mar 13 Applications (pg 166-176) Homework 3 Thursday Apr 6th
Mar 20 Axioms for Homology
Mar 27 Universal Coefficient Theorem
Apr 3 Cohomology Homework 4 Thursday May 4th
Apr 10 No classes Spring Break
Apr 17 No classes Spring Break
Apr 24 Cup Products
May 1 Orientation
May 8 Poincare Duality Homework 5 Thursday May 18th
May 15 ???


Useful Links:
  1. Previous Qualifying Exams
  2. Triangulations of manifolds
  3. Triangulation of surfaces
  4. Classification of surfaces: Conway's ZIP proof     Zeeman's proof
  5. Finitely generated abelian groups
  6. CUNY Geometry and Topology Seminar
  7. Geometry and Topology Student Seminar
  8. Knot Theory (Math 82800)