A link polynomial via wall crossings
نویسنده
چکیده
Given an oriented link L in 3-space we consider a generic homotopy connecting L with the unlink. To each singular link in the homotopy we associate some polynomial using an extension of the Kauffman bracket. The signed sum of these polynomials is a new link invariant, called Cross(L). It is determined by the following skein relations: Cross(unlink) = 0 Cross(L+)− Cross(L−) = t −1/2V (L+) + t 1/2V (L−) + V (L0). Here, V denotes the Jones polynomial with its usual variable t. The framed version of Cross(L) leads to a 1-cocycle for some singular knot space and could possibly give other knot polynomials. 1
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