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Week of...
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Links
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Sep 11
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About, Tue, Thu
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Sep 18
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Tue, Kurlin(P), Thu
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Sep 25
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Tue, Photo, Thu
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Oct 2
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HW1, Tue, Thu
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5
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Oct 9
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Tue(P), Thu(P)
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Oct 16
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HW2, Tue(P), Thu(P)
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7
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Oct 23
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Tue(P), Thu
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Oct 30
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HW3, Tue, Thu
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9
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Nov 6
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Tue ( ), Thu
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10
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Nov 13
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Tue, Thu
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11
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Nov 20
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HW4(P), Thu
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12
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Nov 27
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Thu
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13
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Dec 4
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Syzygies in Asymptote, Final
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Jan 8
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Grades
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Note. (P) means "contains a problem that Dror cares about".
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![06-1350-ClassPhoto.jpg](/images/thumb/7/7f/06-1350-ClassPhoto.jpg/210px-06-1350-ClassPhoto.jpg) Add your name / see who's in!
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On to 07-1352
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Solve the following problems and submit them in class by November 2, 2006:
Question 1. Let
denote the writhe (self linking number) of a band knot
.
- Is
a finite type invariant? Of what type?
- In what sense is
"made of finite type invariants"?
- Compute the weight system of
.
Question 2. Recall the HOMFLY-PT polynomial, given by the recursive definition
Failed to parse (unknown function "\overcrossing"): {\displaystyle q^{N/2}H\left(\overcrossing\right)-q^{-N/2}H\left(\undercrossing\right)=(q^{1/2}-q^{-1/2})H\left(\smoothing\right) }
and by the initial condition
=1.
- In what sense is
a finite type invariant?
- Compute the weight system of
.
Question 3.
- Find a concise algorithm to compute the weight system associated with the Lie algebra
in its defining representation.
- Verify that your algorithm indeed satisfies the
relation.
Don't submit the following, but do think about it:
Question 4. Read Dror's article Lie Algebras and the Four Color Theorem and convince yourself that it is, after all, a worthless curiosity.