Week of May 18th: 35 pages of reading.
Fundamental Group
Pages 21-56: Basic Constructions in the fundamental group, Van Kampen's Theorem.
Problems: Basic Constructions: 1,3,5,8,11,12,13,16, and 18.
Problems: Van Kampen's Theorem: 3,4,7,8,12,13,14, 16, and 20.
Week of May 26th: 27 pages of reading.
Covering Spaces
Pages 56-83: Introduction, Lifting Properties, Classifying Covering Spaces, Deck Transformations and Group Actions, LOTS OF EXAMPLES WORKED OUT HERE!
Problems: 1,4,5,7,9,10,13,14,18,20,26, and 30.
Week of June 2nd: 33 pages of reading.
Introduction to Homology Theory
Pages 97-108:Simplicial Homology
Pages 108-113: Singular Homology
Pages 113-115: Exact Sequences, Excision
Pages 115-126: Relative Homology Groups
Pages 128-130: Equivalence of Different Homologies
Problems: 11, 13, 14,15,16,26, and 27.
Week of June 9th: 20 pages of reading.
Computations and Applications in Homology
Pages 134-137: Degree of a map
Pages 137-146: Cellular Homology, LOTS OF EXAMPLES
Pages 146-148: Euler Characteristic, Split Exact Sequences.
Pages 149-153: Mayer-Vietoris Sequences
Pages 153-154: Homology with (other) Coefficients
Problems: 1,2,4,6,9,10,11,12,19,20,21,22,23,28,31, and 32
Week of June 16th: 12 pages of reading.
Homology Potpourri
Pages 162-165: Intro to Category Theory (just read).
Pages 166-168: The relationship between Homology and Fundamental Group.
Pages 177-183:Simplicial Approximations (LOTS OF EXAMPLES).
Problems:.
Week of June 23rd: 21 pages of reading.
Cohomology
Pages 185-190: Introduction and definitions.
Pages 190-197: The Universal Coefficient Theorem
Pages 197-206: Cohomology Groups.
Problems:
Week of June 30th-first week of July: 23 pages of reading.
Pages 230-249: Poincare' Duality
Pages 253-257:Collar Neighborhoods and Alexander duality
Problems: