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## The wClips |
http://katlas.math.toronto.edu/drorbn/dbnvp/dbnvp.png |

Date | Links |
---|---|

Jan 11, 2012 | 120111-1: Introduction. 120111-2: Section 2.1 - v-Braids. |

Jan 18, 2012 | 120118-1: An introduction to this web site. 120118-2: Section 2.2 - w-Braids by generators and relations and as flying rings. 120118-3: Section 2.2 - w-Braids - other drawing conventions, "wens". |

Jan 25, 2012 | 120125-1: Section 2.2.3 - basis conjugating automorphisms of . 120125-2: A very quick introduction to finite type invariants in the "u" case. |

Feb 1, 2012 | 120201: Section 2.3 - finite type invariants of v- and w-braids, arrow diagrams, 6T, TC and 4T relations, expansions / universal finite type invariants. |

Feb 8, 2012 | 120208: Review of u,v, and w braids and of Section 2.3. |

Feb 15, 2012 | 120215: Section 2.5 - mostly compatibilities of , also injectivity and uniqueness of . |

Feb 22, 2012 | 120222: Section 2.5.5, , and Section 3.1 (partially), the definition of v- and w-knots. |

Feb 29, 2012 | 120229: Sections 3.1-3.4: v-Knots and w-Knots: Definitions, framings, finite type invariants, dimensions, and the expansion in the w case. |

Mar 7, 2012 | 120307: Section 3.5: Jacobi diagrams and the bracket-rise theorem. |

Mar 14, 2012 | 120314: Section 3.6 - the relation with Lie algebras. |

Mar 21, 2012 | 120321: Section 4 - Algebraic Structures. |

Mar 28, 2012 | Out-of-sequence not-on-tape we watched the video of Talks: GWU-1203. |

Apr 4, 2012 | 120404: Section 3.7 - The Alexander Theorem (statement). |

Apr 18, 2012 | 120418: Aside on the Euler trick, the differential of , and the BCH formula. |

Apr 25, 2012 | 120425: Section 3.8, a disorganized lecture towards the proof of the Alexander theorem. |

May 2, 2012 | 120502: Section 4: Algebraic structures (review), circuit algebras, v- and w-tangles. |

May 10, 2012 | 120510: Sections 5.1 and 5.2: tangles, their projectivization and its relationship with Alekseev-Torossian spaces. |

May 23, 2012 | 120523: Section 5.2: Proof of the relationship with A-T spaces. |

May 30, 2012 | 120530: Interpreting as a universal space of invariant tangential differential operators. |

Group photo on January 11, 2012: DBN, ZD, Stephen Morgan, Lucy Zhang, Iva Halacheva, David Li-Bland, Sam Selmani, Oleg Chterental, Peter Lee. |

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When talking about powers of the augmentation ideal, we only use the original operations of our structure.

So in the example where the structure is a group $G$, its group-ring ${\mathbb Q}G$ is again a structure with just one binary operation (multiplication) plus an artificially-added auxiliary operation "addition" which does not participate in taking powers of the augmentation ideal.

An alternative to all that is to start with a structure whose ${\mathcal O}_\alpha$'s are linear spaces (or at least, ${\mathbb Z}$-modules) and all of whose operations are multi-linear. Here again "addition" will have a special role and will not participate in forming powers of the augmentation ideal. --Drorbn 15:46, 25 March 2012 (EDT)