Algebraic Topology (math875) Fall 2005

Lecture: Time: Tuesday and Thursday 8:05-9:20am. Room: Cardwell-Hall 131

Syllabus including homework assignments. Syllabus as PDF file

Exam: The exam for this course was in form of an additional set of homework problems. These homework problems was given to the students on Monday December 12 and was due Monday December 19 at noon.

Literature:

We followed mainly the book

A. Hatcher, Algebraic Topology, Cambridge University Press (2002). There is a homepage for this book including a list of corrections.
The book was supplemented by a small note on CW-complexes.

Good reference books on point set topology are:

M. A. Armstrong, Basic Topology, Undergraduate Texts in Mathematics, Springer--Verlag (1983).

J. Dugundji, Topology, Allyn and Bacon, Inc. (1966).

K. Janich, Topology, Undergraduate Texts in Mathematics, Springer--Verlag (1984). Translation from original German edition {\it Topologie}, Springer--Verlag (1980).

The books of Armstrong and Janich have some flavor of basic algebraic topology.

Some other books on algebraic topology are:

A. Dold, Lectures on Algebraic Topology, Spinger--Verlag (1995). Reprint of the 1972 edition.

W. S. Massey, Algebraic Topology: An Introduction, Graduate Texts in Mathematics {\bf 56}, Springer--Verlag (1977).

E. H. Spanier, Algebraic Topology, McGraw--Hill, Inc.\ (1966).

J. W. Vick, Homology Theory, Graduate Texts in Mathematics {\bf 145}, Springer--Verlag (1994).

Massey's book is a very good reference on the fundamental group. There is a newer and expanded version of this book which also treats homology theory. The book of Vick gives a good and rather quick introduction to homology and cohomology theory without leaving details unproved. In addition there is a chapter on covering space theory. Spanier's book is the classical reference book in algebraic topology.