Basic Topology
Math 608
Spring, 1998
INSTRUCTOR: Laurence Taylor PHONE: 17468
OFFICE: 232 CCMB
EMAIL: taylor.2@nd.edu
Assignments are here.
This is the second semester of a yearlong course designed to cover
the Candidacy Syllabus in Topology, or at least most of it.

Homology Theory:
 Singular homology and cohomology theory.
 EilenbergSteenrod axioms.
 The cohomology ring.
 Homology calculations via CW complexes.
 Calculation of the cohomology ring of projective spaces.
 Homotopy Theory:
 Exact homotopy sequence of a pair.
 Hurewicz's Theorem.
 Manifolds. The Poincare Duality Theorem.
Prerequisites:
Math 607 (or consent of the Instructor).
Main reference:

Munkres, Elements of Algebraic Topology
Additional references:

Dold, Lectures on Algebraic Topology

Fulton, Algebraic Topology

Greenberg and Harper, Lectures on Algebraic Topology

Massey, A Basic Course in Algebraic Topology

Maunder, Algebraic Topology

Spanier, Algebraic Topology

Vick, Homology Theory

Whitehead, Homotopy Theory