Constructing Knot Tunnels Using Giant Steps
نویسندگان
چکیده
In [6], Goda, Scharlemann, and Thompson described a general construction of all tunnels of tunnel number 1 knots using “tunnel moves”. The theory of tunnels introduced in [3] provides a combinatorial approach to understanding tunnel moves. We use it to calculate the number of distinct minimal sequences of such moves that can produce a given tunnel. As a consequence, we see that for a sparse infinite set of tunnels, the minimal sequence is unique, but generically a tunnel will have many such constructions.
منابع مشابه
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