Return to Chuck Livingston's home page

The following is a list of comments concerning exercises. For comments and errata concerning references, mathematics, or a page by page listing, select the desired option.

(p. = Page, e. = Exercise, l. = Line, t. = Theorem, c. = Corollary, f. = Figure, d. = Definition.)

• p.10, e.7: The deformation is quite difficult to find; Perko's paper, listed in the reference has a series of figures illustrating it.
• p.26, e.5.5: Here "inversion" means a deformation of the knot to its reverse.
• p.32, e.1.2: Deform the illustrated knot into a standard picture of the unknot, using only Reidemeister moves.
• p.35, e.2.2: n is the number of half twists; for example, in Figure 3.6a, n is the number of crossings.
• p.36, e.2.4b: Theorem 2, not 1. e.2.4d: Theorem 2, not 1. Also, in Figure 3.7 the diagram on the left illustrates a right-handed crossing.
• p.88, e.1.7b: (1,5,3,4) is the product of three transpositions, not four.
• p.94, e.2.2: Only one of the labelings is correct, not two.
• p.99, e.3.4: Knot 6_1 cannot be labeled with transposition, but can be labeled with 4-cycles. Knot 9_46 can be labeled in both ways, not just with transpositions. (The point remains the same; these knots are distinguished using S_4 labelings only if the conjugacy classes of labels are considered.)
• p.104, e.4.1: The second relation is clearly wrong. Check the relations on p.101.
• p.123, e.3.9: Reference should be Exercise 1.5, not 2.5.
• p.140, e.3.4: One can assume p is always positive. In this case, the knots are equivalent if and only if q - q' = 0 mod p, or qq' = 1 mod p.

Return to Chuck Livingston's home page