Degree Sequence for Non-Compact Knots

Rama Mishra �� �iIndian Institute of Technology�j

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�T�v�FVassiliev introduced the notion of non-compact knots (embedding of R in R³) for computing new invariants. It was observed that any non-compact knot is equivalent to a Polynomial embeddings. Thus, given a Knot-type finding out three polynomials f(t), g(t) and h(t) such that the map t --> (f(t), g(t), h(t)) can represent it will be a useful proposition. If deg f(t) =l, deg g(t) = m and deg h(t) = n we way that (l, m, n) is a degree sequence for the given Knot-type. If (l, m, n) is minimal with this property then we say that it is the minimal degree sequence. We will discuss the issue of finding out a degree wequence and the minimal degree sequence for given Knot-types.

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