Topology
If you know nothing about topology, read the start of
a point-set topology book before trying to tackle algebraic
or piecewise-linear topology. Some background in
real analysis
and/or geometry
is probably helpful, though you can probably get away without
it if you have sufficient mathematical maturity.
Point-Set Topology
- Munkres, J. R., (1975) Topology: A First Course,
Prentice-Hall, Englewood Cliffs, NJ.
- Willard, Stephen (1970) General Topology, Addison-Wesley, Reading MA.
Algebraic Topology
- Bredon, Glen E. (1993) Topology and geometry, Springer-Verlag,
New York.
- Munkres, James R. (1984)
Elements of Algebraic Topology, Addison-Wesley, Menlo Park, CA.
- Massey, William S. (1980) Singular Homology Theory,
Graduate Texts in Mathematics 70, Springer-Verlag, New York.
- Massey, William S. (1967) Algebraic Topology: An Introduction,
Springer-Verlag, New York.
Piecewise-Linear Topology
- Rourke, Colin Patrick and Brian Joseph Sanderson (1982) Introduction to
Piecewise-Linear Topology, Springer Study Edition,
Springer-Verlag, New York
(ISBN 0-387-11102-6, paperback).
Knot Theory
- Adams, Colin C. (1994) The Knot Book: An Elementary Introduction to the
Mathematical Theory of Knots, W.H. Freeman, NY.
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