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{{note|Bar-Natan_97}} D. Bar-Natan, ''Non-associative tangles,'' in ''Geometric to {{note|Bar-Natan_Le_Thurston_03}} D. Bar-Natan, T. Q. T. Le and D. P. Thurston, ''

== class note ==

....math.toronto.edu/drorbn/index.php?title=Image:Lecture3_1.jpg September 19 Note (1/5)] ....math.toronto.edu/drorbn/index.php?title=Image:Lecture3_2.jpg September 19 Note (2/5)]

...se are not necessary for the statement of the theorem, it is worthwhile to note that the invariants of the unknot, the unknotted <math>\theta</math>-graph {{note|BGRT}} D. Bar-Natan, S. Garoufalidis, L. Rozansky and D. P. Thurston, ''Whe

This is another "testing" note.

...-Natan for the Fall Session of MAT240 at the University of Toronto. Please note that this set is missing a diagram that could not be converted to PDF form. ...e lecture given on December 3rd by Professor Natan (in PDF format). Please note that there is an important diagram missing from this file. This is because

Note that the y axis and x axis in ordinary coordinate plane will become Img axi Image:Sept 20 class note scan1.jpg|Page 1

'''Note.''' The last $z$ on this blackboard should be a $z_i$.

Note that as a matter of policy I answer all general-interest questions posted o

...handout is not necessary! It is enough that <math>Z</math> be invertible. Note also that contrary to the handout, it is not known that the simultaneous ne

(Note: This can also be done abstractly, i.e. without choosing a basis, but then

{{note|Bar-Natan_95}} D. Bar-Natan, ''On the Vassiliev knot invariants,'' Topology {{note|Bar-Natan_96}} D. Bar-Natan, ''Some computations related to Vassiliev invar

Note that $c_j$ goes to $u_iw_j$, not to $0$.

...certificate of recognition. If you are interested in becoming a volunteer note-taker, please take an information form and register online, or visit the Ac

Disclamer: This is a student prepared note based on the lecures of [http://drorbn.net/dbnvp/12-267-120928.php Friday, Note that any function that is Lipschitz is uniformly continuous, and that if a

Note that this algebra is commutative

Note that for <math>n=1,2</math> this is trivial. For <math>n=3</math> we have t ...t of disjoint transpositions. Write <math>\sigma = (123)\sigma'</math> and note that <math>{\sigma'}^2 = e.</math>

== Important Note About This Page ==

The canonical <math>0</math>-framing of knots in <math>\mathbb{R}^3</math> (Note that such canonical identification only exist in <math>\mathbb{R}^3</math>.

File:October 8 note 1.jpeg|page 1 File:October 8 note 2.jpeg|page 2

Typically long equations have no closed form solutions. Yet note that Kurlin first derived the equation and only then found its solution. Wa Here are a few concrete questions to expose my ignorance of simple algebra. Note that <math>f</math> is is a rational function in its variables and their ex

Image:15-344 lecture note for Dec.8 .jpg|Page 1 Image:15-344 lecture note for Dec.8 2 .jpg|Page 2

Note my comments from [[06-240/Homework Assignment 5]]: ...here may be some computations, but nothing that will require a calculator. Note also that I may include some questions from the homework assignments verbat

There's a note by Habiro in which he shows that every strict graph clasper can be replaced

{{Begin Side Note|15%}} {{End Side Note}}

{{note|Le_Murakami_97}} T. Q. T. Le and J. Murakami, ''Parallel Version of the Uni {{note|Murakami_Ohtsuki_97}} J. Murakami and T. Ohtsuki, ''Topological Quantum Fie

...interpreted to mean <math>\sum_{k=0}^\infty\frac{M_i^kh_j^k}{k!}</math>. (Note that the number of formal parameters <math>h_j</math> need not equal the nu Note that an unreasonable algorithm for this question is readily available. Over

{{12-267/Good Deeds|uid=Eyjaffe|points=2|deeds=Video note; 2-3 typo corrections}} '''Note.''' This page is protected. Its [[Talk:12-267/Register of Good Deeds|discus

Much of this note comes from the paper "Finite type invariants of classical and virtual knots Note the additional information in the Gauss diagram about the overpasses and un

It's interesting to note that paracompactness (every open cover has a subcover such that every point

...on of finite groups of order 84. This was a project that I did in MAT 347. Note that there is a mistake when calculating the order of the automorphism grou

{{note|Le_Murakami_97}} T. Q. T. Le and J. Murakami, ''Parallel Version of the Uni {{note|Murakami_Ohtsuki_97}} J. Murakami and T. Ohtsuki, ''Topological Quantum Fie

(Note that when the class photo page was introduced I said there would be '''Note.''' This page is protected. Its [[Talk:09-240/Register of Good Deeds|discus

(Note by [[User:Cameron.martin]]). The unknot $0_1$ and the figure-eight knot $4_

...the topology in question is the trivial topology", or something like that. Note that the resulting topology may also depend on the direction of the line <m

'''Note added March 8, 2008.''' The problem this paperlet addresses remain interest {{note|Bar-Natan}} Dror Bar-Natan, ''[http://www.math.toronto.edu/~drorbn/papers/C

...ular <math>K</math>, <math>Z(K) = D_K +</math> diagrams of higher degree. (Note that a universal finite type invariant is '''not''' an finite type invarian

==Dror's Note==

Considering just the set without the identification, we note this is a group with the operation being concatenation of words followed by Note: <math>G_1 *_H G_2</math> is equivalent to { words in <math>G_1\cap G_2\}/

* Note the unusual time! We will have our next lunch on Wednesday July 2, at the u

Note the conference "Braids in Paris", September 17-20 2008, http://tresses08.in

# Note that we also automatically use the list on meta: http://meta.wikimedia.org/

'''Note.''' By $\partial(g\triangleright e)=g\partial(e)g^{-1}$, the image of $\par

Note 1: As is assumed in this section of the course, our map p is continuous, ou Note 2: Recall that connected does NOT imply locally connected. Indeed recall th

(Note that when the class photo page was introduced I said there would be no pena Note that this page is protected. Its [[Talk:08-401/Register of Good Deeds|discu

== Scanned Lecture Note for September 17 ==

...but submit only the solutions of the problems marked with the letter "S". Note that the word "subring" was not defined in class, but its simple definition

{{note|Drinfeld_90}} V. G. Drinfel'd, ''Quasi-Hopf algebras,'' Leningrad Math. J. {{note|Drinfeld_91}} V. G. Drinfel'd, ''On quasitriangular Quasi-Hopf algebras and

Note: This will be archived once the package is more complete. Note: You could do computations in Free Lie Algebras with more generators if yo

Disclamer: This is a student prepared note based on [http://drorbn.net/dbnvp/12-267-121002-2.php the lecure of Tuesday

File:monday Nov 10.jpg|Nov 10 note

{{Begin Side Note|30%}} {{End Side Note}}

# Prove that <math>O(3)</math> is not solvable (though note that the similarly-defined group <math>O(2)</math> is solvable).

* Note that the numbers <math>1^6-1=0</math>, <math>2^6-1=63</math>, <math>3^6-1=7

{{note|Bar-Natan_97}} D. Bar-Natan, ''Non-associative tangles,'' in ''Geometric to {{note|Drinfeld_90}} V. G. Drinfel'd, ''Quasi-Hopf algebras,'' Leningrad Math. J.

...g}$-like construction". See also {{Home link|People/Haviv/S3g.pdf|Haviv's note}}, where a ''symmetric'' invariant tensor in ${\mathfrak g}^{\otimes 3}$ is

== Lecture Note for September 15 ==

File:monday.jpg|Nov 3 note

(Note that when the class photo page was introduced I said there would be no pena Note that this page is protected. Its [[Talk:07-401/Register of Good Deeds|discu

This note closely follows the introductory parts of "Vassiliev and Quantum Invariants ...te knots, it is known that finite type invariants separate braids. In this note, we describe the process of getting a chord diagram from an m-singular brai

...s.math.toronto.edu/drorbn/dbnvp/257-161201.php today's video]</span>! (And note that your wiki account allows you to comment on specific times within the v

...s.math.toronto.edu/drorbn/dbnvp/257-170330.php today's video]</span>! (And note that your wiki account allows you to comment on specific times within the v

* Note that the numbers <math>1^6-1=0</math>, <math>2^6-1=63</math>, <math>3^6-1=7

'''Note the unusual time, place and content!''' Please let me know if you are plann Note that we will '''not''' have Knot at Lunch meetings on July 9, 16 and 23.

Here is a lecture note for today:

(Note that det(''EA'') = det(''E'')·det(''A'') and that det(''A'') may be writte

...y), a sequence of points in A can converge to only one point at most. Also note that Hausdorff condition is stronger than T1.

===Note===

* Note that the word "indivisibilities" has the largest number of repetitions of a

== lecture note on oct 18, uploaded by [[User:starash|starash]]==

{{note|AT}} A. Alekseev and C. Torossian, The Kashiwara-Vergne conjecture and Drin {{note|BP}} B. Berceanu and S. Papadima, Universal Representations of Braid and Br

:(In all that, note the absence of "cover all the details".)

Note: this proof is incorrect. It does show one of the numbers assigned to the e

'''Note.''' This page is protected. Its [[Talk:10-1100/Register of Good Deeds|discu

Note: It is usefull to "open the black box" and think about the Mayer Vietoris S Note: Technically we need to check at Mayer Vietoris sequence also works for red

...-the-week plan is in {{Pensieve Link|Classes/10-327|my own notes}}, though note that it is an '''optimistic''' plan, and in reality we will likely cover a ...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

...lunch on Wednesday January 16, at the usual place, Bahen 6180, at 12 noon. Note that this is right after Shlomo Sternberg's third lecture at the Fields Ins

...mathbb{R}^m \}_{\alpha \in A}</math> be an atlas for <math>M\!</math>, and note that <math>\{U_\alpha\}_{\alpha \in A}\!</math> is an open cover of <math>M ...corresponding [http://en.wikipedia.org/wiki/Paracompact Wikipedia entry]. Note, in particular, that locally compact, second-countable topological spaces--

(Note that when the class photo page was introduced I said there would be no pena Note that this page is protected. Its [[Talk:06-240/Register of Good Deeds|discu

* Note that the word "indivisibilities" has the largest number of repetitions of a

We note that this is similar to the proof of the fundamental theorem of calculus, w ''Note''

...rily 1:1 as was implied in the earlier naive computations. Furthermore, we note that C_p(X) has an abelian group structure)

* Note that the word "indivisibilities" has the largest number of repetitions of a

In this note, we compute and interpret the structure constants $f_{abc}$ of $so(N)$, as Note that this also gives us the inverses $t^{(ij)(kl)} = const\cdot\delta^{ik}\

{{note|Kauffman}} L. H. Kauffman, ''An invariant of regular isotopy'', Trans. Ame

{{note|MO}} J. Murakami and T. Ohtsuki, ''Topological Quantum Field Theory for the

...on Thursday July 19, 2007, at the usual place, Bahen 6180, at 12 noon. But note that for the three weeks after that I will be traveling (in {{Home Link|Tal

<span style="color: red;">Important.</span> Note the change from an earlier version of this assignment - Franklin Vera and D

Note that a priori the second part of this question is an order of magnitude har

Though note that under the same circumstances we do not mod out by <math>b^{-1}\bar b_1

...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag ...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

Note that if one tried to pushforward sets A in X, the set operations compliment It is very important to note that the <math>\varphi_0</math> and <math>\psi_0</math> are NOT the charts

===A note from the TA===

{{note|Bar-Natan_Garoufalidis_96}} Dror Bar-Natan and Stavros Garoufalidis, ''[htt

We note that this is obviously continuous and we get uniform convergence to a conti Note: Manifolds are paracompact

* Note that the word "indivisibilities" has the largest number of repetitions of a

'''Solve''' problems <u>10</u>, <u>12</u>, 13, 14abd, <u>14ce</u>, <u>15</u> (note, add "at most" before the "<math>k-1</math>"), <u>16</u>, and 18 in section

Note that these problems largely concern with material that we will not cover in

...here may be some computations, but nothing that will require a calculator. Note also that I may include some questions from the homework assignments verbat

'''Note.''' This page is protected. Its [[Talk:11-1100/Register of Good Deeds|discu