By Solomon Lefschetz

**Read or Download Algebraic Topology (Colloquium Pbns. Series, Vol 27) PDF**

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**Additional resources for Algebraic Topology (Colloquium Pbns. Series, Vol 27) **

**Example text**

We shall return to the specifics of the construction of the Jones polynomial via the bracket polynomial model in section 5, but it is now possible to indicate this model as an amplitude by specifying its matrices. They are (Mab) = (Mab) = M where M is the 2 x 2 matrix (with ii=-1) M = 0 iA iA10 Note that MM = I where I is the identity matrix . amplitude for the circle is E MabMab = (iA)2 + = Note also that the EMabMab = E (Mab)2 (-iA-1)2 = - A2 - A-2. The matrix R is then defined by the equation Rabcd = AMabMcd + AIacIbd , or diagrammatically by R=A^ +A-1 Since, diagrammatically , we identify R with the crossing this equation can be written symbolically as Taken together with the loop value of -A2 - A-2, this equation can be regarded as a recursive algorithm for computing the amplitude.

That is, we assume that following sum is equal to one, for each k from 1 to n-1: Ic(k)1>

Approximate the change according to Fact 1, and regard the point x as the place of curvature evaluation . Let b