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A polynomial which is not necessarily an invariant of a link. It is related to the dichroic polynomial. It is defined by the skein relationship ...

Let E be the largest and e the smallest power of l in the HOMFLY polynomial of an oriented link, and i be the braid index. Then the Morton-Franks-Williams inequality holds, ...

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

Let K_1^n and K_2^n be disjoint bicollared knots in R^(n+1) or S^(n+1) and let U denote the open region between them. Then the closure of U is a closed annulus S^n×[0,1]. ...

Consider two closed oriented space curves f_1:C_1->R^3 and f_2:C_2->R^3, where C_1 and C_2 are distinct circles, f_1 and f_2 are differentiable C^1 functions, and f_1(C_1) ...

Two links can be continuously deformed into each other iff any diagram of one can be transformed into a diagram of the other by a sequence of Reidemeister moves.

A tree of links obtained by repeatedly choosing a crossing, applying the skein relationship to obtain two simpler links, and repeating the process. The tree depth of a ...

Markov's theorem states that equivalent braids expressing the same link are mutually related by successive applications of two types of Markov moves. Markov's theorem is ...

Let V=R^k be a k-dimensional vector space over R, let S subset V, and let W={w in V:w·n^^=0} be a subspace of V of dimension k-1, where n^^ is a unit normal vector of W. Then ...

For a connection A and a positive spinor phi in Gamma(V_+), Witten's equations (also called the Seiberg-Witten invariants) are given by D_Aphi = 0 (1) F_+^A = ...