MATH 495: KNOT THEORY, HOMEWORK 3
CLASSICAL INTEGER INVARIANTS
Due in class, Thursday, 2/20
Problems (to turn in).
(1) Give a construction of a knot that has a non-trivial mod 101 labeling.
(2) Find the number of mod 7 labelings of the knot 52 .
(3) Find
MATH 495: KNOT THEORY, HOMEWORK 1
EQUIVALENCE OF KNOTS
Due at start of class, Tuesday, 2/11
Problems (to turn in).
(1) Show that the trefoil can be deformed so that its (non-regular projection) has exactly
one multiple point. Is this true for all knots?
(
MATH 495: KNOT THEORY, HOMEWORK 5
ADDITIVITY OF CROSSING NUMBER AND MANIFOLDS
Due in class, Tuesday, 3/18
Problems (to turn in).
(1) Prove that if K1 and K2 are alternating knots, then c(K1 #K2 ) = c(K1 ) + c(K2 ).
(2) Prove that the unit circle in R2 is
MATH 495: KNOT THEORY, HOMEWORK 1
EQUIVALENCE OF KNOTS
Due at start of class, Tuesday, 2/4
Problems (to turn in).
(1) Suppose a knot lies in a plane and bounds a convex region in the plane. (Convex means
that any segment with endpoints in the region is en
MATH 495: KNOT THEORY, HOMEWORK 4
THE KAUFFMAN BRACKET AND THE JONES POLYNOMIAL
Due in class, Thursday, 3/6
Problems (to turn in).
(1) Calculate fD (A) for both the left handed and the right handed trefoil.
(2) Find a formula for the Kauman bracket of a c