Projects and Assignments in Pure Mathematics
Knot Theory
A knot is a closed, non-self-intersecting curve in 3-space.
The main problem is to determine whether a given curve can
be deformed into a planar circle, the "unknot". This problem remains
an active focus of research, and is, so far, unresolved. It
can be approached purely combinatorially:
a polynomial can be assigned to
a knot in such a way
that if 2 knots have different polynomials then it is not possible
to
deform one knot into the other.
However,
to really appreciate the subject there is a significant topological angle
which can be explored in a longer project.
Books
N.D. Gilbert and T. Porter, Knots and Surfaces.
C.C.Adams, The Knot Book.
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