Basic Topology
Math 608
Spring, 1998
INSTRUCTOR: Laurence Taylor PHONE: 1-7468
OFFICE: 232 CCMB
EMAIL: taylor.2@nd.edu
Assignments are here.
This is the second semester of a year-long course designed to cover
the Candidacy Syllabus in Topology, or at least most of it.
-
Homology Theory:
- Singular homology and cohomology theory.
- Eilenberg-Steenrod 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
