Blackboard Shots with Prefix "wClips"

120620-132027: Future plans.

120530-135829: R3 as a composition of diffeomorphisms (2).

120530-135516: R3 as a composition of diffeomorphisms.

120530-135145: R as a diffeomorphism (2).

120530-134642: R as a diffeomorphism.

120530-133843: The adjoint and div (2).

120530-133616: The adjoint and div.

120530-132304: Verifying that the bracket goes to the commutator (2).

120530-132037: Verifying that the bracket goes to the commutator.

120530-131156: The tangential vector fields.

120530-130716: The map into differential operators.

120530-125218: Review of wheels, trees, div, and j.

120523-135927: div (3).

120523-135531: div (2).

120523-134654: div.

120523-133943: The splitting.

120523-133509: Comparing the brackets, more conceptually (2).

120523-133050: Comparing the brackets, more conceptually.

120523-132729: Comparing the brackets (5).

120523-132320: Comparing the brackets (4).

120523-131621: Comparing the brackets (3).

120523-130834: Comparing the brackets (2).

120523-130329: Comparing the brackets.

120523-125831: Primitives, wheels, and trees (4).

120523-125534: Primitives, wheels, and trees (3).

120523-125424: Primitives, wheels, and trees (2).

120523-124956: Primitives, wheels, and trees.

120510-140700: ${\mathcal A}^w$ and Alekseev-Torossian spaces (2).

120510-135047: Wheels and trees (2).

120510-134619: Wheels and trees.

120510-134243: Milnor-Moore and primitives.

120510-133424: ${\mathcal A}^w$ and Alekseev-Torossian spaces.

120510-132343: Proof of head invariance.

120510-131406: Bracket rise for w, head invariance.

120510-130722: Bracket rise for w.

120510-130448: v-Tangles, w-Tangles, their candidate projectivizations, and the w-expansion.

120510-130052: v-Tangles, w-Tangles, and their candidate projectivizations.

120502-134819: v-Tangles and w-Tangles.

120502-134627: Circuit Algebras with Skeleta.

120502-133941: Examples of Circuit Algebras (2).

120502-133529: Examples of Circuit Algebras.

120502-132813: Circuit Algebras.

120502-132309: Wiring diagrams (2).

120502-131940: Wiring diagrams.

120502-131204: Review of $\mathcal A$-Expansions (2).

120502-130529: Review of $\mathcal A$-Expansions.

120502-130049: Review of Expansions (3).

120502-125327: Review of Expansions (2).

120502-125022: Review of Expansions.

120502-124716: Review of Algebraic Structures.

120425-140422: Relations between $\Lambda$ and $Y$.

120425-140058: $\Lambda$.

120425-135210: The IAM Relations.

120425-132710: E(LHS).

120425-130406: E(RHS).

120425-124359: Dreams on an Alexander homology.

120418-135500: The BCH Formula (3).

120418-134601: The BCH Formula (2).

120418-133856: The Differential of the Exponential Function (3).

120418-133226: The Differential of the Exponential Function (2).

120418-132328: The Differential of the Exponential Function.

120418-131408: The BCH Formula.

120418-130327: The Euler Trick (3).

120418-125634: The Euler Trick (2).

120418-125036: The Euler Trick.

120418-124645: Detached wheels and hairy Y's.

120418-124122: Statement of the Alexander Theorem.

120404-130233: EZ.

120404-125832: The Euler operator.

120404-125306: Exercise 3.21: Detached wheels and hairy Y's.

120404-124504: Exercise 3.20: Commutators Commute.

120404-123625: A simplified version of the w-Alexander theorem.

120404-122952: The w-Alexander theorem (Theorem 3.27).

120404-122243: A classical formula for the Alexander polynomial.

120404-120711: A conjectured formula for the Alexander polynomial.

120404-115926: The trapping matrix.

120404-115032: What's $Z^w$ on knots?

120328-152816: Bicrossed scratch.

120321-140025: Homomorphic expansions.

120321-135847: Expansions.

120321-135345: Quandles and Leibniz algebras (5).

120321-134725: Quandles and Leibniz algebras (4).

120321-133830: Quandles and Leibniz algebras (3).

120321-133421: Quandles and Leibniz algebras (2).

120321-132900: Quandles and Leibniz algebras.

120321-132356: Quandles defined (2).

120321-131614: Quandles defined.

120321-131212: Groups and associative algebras.

120321-130513: Operations on proj.

120321-130125: ${\mathcal I}^m$ and the projectivization.

120321-125146: The augmentation ideal.

120321-124643: Examples - Actions, Quandles, QTGs, fibered situations.

120321-124229: Examples - groups and group homomorphisms.

120321-123740: Algebraic Structures.

120314-140441: The 2D example and ${\mathcal T}$ (2).

120314-140017: The 2D example and ${\mathcal T}$.

120314-135504: ${\mathcal T}$ descends to ${\mathcal A}^{wt}$ (4).

120314-134812: ${\mathcal T}$ descends to ${\mathcal A}^{wt}$ (3).

120314-134227: ${\mathcal T}$ descends to ${\mathcal A}^{wt}$ (2).

120314-133959: ${\mathcal T}$ descends to ${\mathcal A}^{wt}$.

120314-133340: The map ${\mathcal T}$.

120314-132622: The 2D example.

120314-131943: The co-commutative case.

120314-131527: The double is metrized (4).

120314-130813: The double is metrized (3).

120314-130520: The double is metrized (2).

120314-130022: The double is metrized.

120314-125800: What is $I{\mathfrak g}$? (2)

120314-125144: What is $I{\mathfrak g}$?

120314-124450: The tensor map claim.

120314-123935: ${\mathcal A}^w$ and ${\mathcal A}^{wt}$.

120307-140335: ${\mathcal A}^w(\bigcirc)$ (2).

120307-135824: ${\mathcal A}^w(\bigcirc)$.

120307-135109: Proof of bracket-rise (3).

120307-134836: Proof of bracket-rise (2).

120307-134130: Proof of bracket-rise.

120307-132355: Caravans of wheels and trees.

120307-131928: Wheels and trees.

120307-130936: The "bracket-rise" theorem.

120307-130443: ${\mathcal A}^{wt}$.

120307-124327: $Z^w$ is well-defined.

120307-124140: $Z^w$.

120229-135002: The Milnor-Moore theorem.

120229-134612: The product and the co-product.

120229-134106: ${\mathcal A}^{v,w}(\uparrow)$ and ${\mathcal A}^{v,w}(\bigcirc)$.

120229-133825: $\alpha:{\mathcal A}^u\to{\mathcal A}^v$.

120229-133213: 4T.

120229-132915: 6T.

120229-132549: ${\mathcal A}^{v,w}$.

120229-132431: Type $m$ invariants and their weight systems.

120229-132021: Semi-virtual crossings.

120229-130442: Framed and unframed long v-knots: proofs.

120229-130311: Framed and unframed long v-knots: the compositions.

120229-125332: Framed and unframed long v-knots: $h$.

120229-124714: Framed and unframed long v-knots: $\iota$ and $sl$.

120229-124547: Classical linkinf and self-linking numbers.

120229-124517: Framed and unframed long v-knots, day 2.

120222-133119: Framed and unframed long v-knots.

120222-132410: The self-linking numbers (2).

120222-131844: The self-linking numbers.

120222-130333: ${\mathcal K}^v$ is a non-Abelian monoid.

120222-130027: Long v-Knots and circular v-Knots.

120222-125634: u-Knots, v-Knots, w-Knots.

120222-124827: There's no $Z$ compatible with $\alpha$.

120222-124329: $\alpha:{\mathcal A}^u\to{\mathcal A}^w$.

120215-140055: 2.5.3 Uniqueness of a well-behaved homomorphic expansion.

120215-135838: 2.5.2 Injectivity; 2.5.3 Non-uniqueness in the non-homomorphic case.

120215-135308: 2.5.1.5 Compatibility with the action on the free group (2).

120215-134523: 2.5.1.5 Compatibility with the action on the free group.

120215-133809: 2.5.1.6 Non-compatability with strand doubling/unzipping.

120215-133052: 2.5.1.4 Compatibility with strand deletions (2).

120215-132709: 2.5.1.4 Compatibility with strand deletions.

120215-132242: 2.5.1.3 Compatibility with strand insertions.

120215-131538: The Magnus and the exponential expansions for the free group.

120215-130448: 2.5.1.2 Compatibility with braids cloning (2).

120215-125912: 2.5.1.2 Compatibility with braids cloning.

120215-125131: 2.5.1.1. Compatibility with braid invertion.

120215-123443: Review of $G\to{\mathcal A}^Q(G)$ and functoriality.

120208-140123: Checking R3 for $Z^w$.

120208-135721: uvw Table (5).

120208-135214: Expansions and homomorphic expansions.

120208-134550: Deriving 4T-Arrow.

120208-134035: Deriving 4T.

120208-133640: uvw Table (4).

120208-133300: Deriving locality and tails-commute.

120208-132729: Deriving the 6T relation.

120208-131944: uvw Table (3).

120208-131634: Generating $I^n/I^{n+1}$ (2).

120208-130902: Generating $I^n/I^{n+1}$.

120208-130150: Semi-virtuals crossings and their arrows.

120208-125305: Singular braids and chord diagrams.

120208-124632: uvw Table (2).

120208-124221: uvw Table.

120201-140238: Z^w.

120201-135822: Homomorphic QUFTI.

120201-135630: The fundamental theorem and QUFTI (3).

120201-135220: The fundamental theorem and QUFTI (2).

120201-134536: The fundamental theorem and QUFTI.

120201-134345: The "central" question of FTI.

120201-133806: QUFTI as filtered maps (2).

120201-133441: QUFTI as filtered maps.

120201-133243: gr is a functor.

120201-132843: Quadratic Universal Finite Type Invariant(s) (QUFTI).

120201-132314: A^w.

120201-131843: A^v.

120201-131250: 6T / CYB.

120201-130713: Quadratic relations.

120201-130408: Arrow diagrams (2).

120201-130036: Arrow diagrams.

120201-125709: What are the generators? What are the relations?

120201-125045: The PvBn case.

120201-124604: Type p invariants.

120201-124249: The augmentation ideal and its powers.

120125-140415: Chord diagrams for braids.

120125-140131: Chord diagrams for knots.

120125-135825: The top derivative is constant.

120125-135010: The definition of finite-type invariants.

120125-134559: Resolving double points.

120125-132756: The two actions of PvB_n (2).

120125-132316: The two actions of PvB_n.

120125-131956: No semi-direct structure in the w case.

120125-131513: The "u" case.

120125-130948: The action in the pure case.

120125-130706: The action on the product of all generators.

120125-130211: The action of real crossings (2).

120125-130204: The action of real crossings.

120125-124729: The action of virtual crossings.

120125-124134: Action by conjugation.

120125-123642: McCool's Theorem.

120125-122827: Artin's theorem.

120118-135356: A presentation with wens (2).

120118-134845: A presentation with wens.

120118-133727: Non-horizontal flying rings.

120118-133344: Ribbon singularities.

120118-130809: Horizontal flying rings as a fundamental group.

120118-125803: wB_n.

120118-125435: UC and OC.

120118-125422: The "\sigma_{ij}" presentation of PvB_n.

120118-125101: The "Yang-Baxter" relation.

120118-124119: v-Braids, again.

120111-140241: The wrong definition of uB_n is the right definition of vB_n.

120111-135722: vB_n as a semi-direct product with S_n.

120111-134813: Overcrossings don't commute and undercrossings don't commute.

120111-133959: The detour move.

120111-133952: vB_n.

120111-130844: A knot on a surface.

120111-130836: u, v, and w.

120111-130829: Topology, combinatorics, low algebra, high algebra.