MAT 1300 Y (MAT 427S)
Topology
TR 10-11:30, SS 5017A
Teaching assistant:
Ana Maria Savu
Marking scheme for MAT 1300: The course mark will be based on
10 homework assignments (equally weighted, total weight 50 %) and a final
exam (worth 50 %).
The final exam
will be on April 22, 13:00--15:00 in Room SS 1083.
Marking scheme for MAT 427S: Undergraduate students taking only the
second half of the course: The course mark will be based on five
homework assignments, all carrying equal weight.
The homework problems will be posted bi-weekly at the bottom
of this webpage. They are due in class on the indicated due date -- no
extensions are given unless there are truly important reasons.
Course outline:
- Point set topology: Topological spaces and
continuous functions, connectedness and
compactness, countability and separation
axioms.
- Homotopy: Fundamental group, Van
Kampen theorem, Brouwer's theorem for the
2-disk, Homotopy of spaces and maps, higher
homotopy groups. Covering theory, universal
coverings, group actions, CW-complexes,
graphs.
- Homology: Simplicial and singular
homology, homotopy invariance, exact
sequences, Mayer-Vietoris, excision, Brouwer's
theorem for the n-disk.
- Cohomology: Cohomology groups, cup
products, cohomology with coefficients.
- Topological manifolds: Orientation,
fundamental class, Poincare duality.
Reference:
Hatcher: Algebraic Topology, Cambridge University Press, 2001.
The paperback version of this book costs 49.50 Canadian Dollar, according to
this website.
It can be viewed online at the
author's website.
The first part of this course is also well-covered in the new edition of
Munkres: Topology: a first course,
The book is priced at 126.95 Canadian Dollar, according to this website.
Additional References:
Kelley: General Topology, Springer, 1975.
Bredon:
Topology and Geometry, Springer, 1993.
Munkres: Elements of Algebraic
Topology, Perseus Books, 1993.
Fulton:
Algebraic Topology: A First Course, Springer,
1994.
Bott, Tu: Differential Forms in
Algebraic Topology, Springer, 1997.
A brief history of topology can be found
here.
