Dror Bar-Natan: Classes: 2003-04: Math 1350F - Knot Theory:

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Homework Assignment 8: Primitives; W(L) is well defined

Assigned Thursday November 6; due Thursday November 13 in class.

This document in PDF: HW.pdf

To be handed in. Recall that the primitives of ${\mathcal A}$ are the connected diagrams. Prove that they generate ${\mathcal A}$ -- that every element of ${\mathcal A}$ is a sum of products of primitives.

Recommended for extra practice. Check that indeed $W_{L,\langle\cdot,\cdot\rangle,R}:{\mathcal A}\to{\mathbb{F}}$ is well defined. (I.e., does not depend on the all choices (especially the bases) and vanishes on AS, STU and IHX).

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