User:Drorbn/06-1350-HW4: Difference between revisions
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|[[Image:06-1350-BPlus.svg]] |
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===The Relations=== |
===The Relations=== |
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====The Reidemeister Move R3==== |
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The picture is |
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[[Image:06-1350-R4.svg|400px|center]] |
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In formulas, this is |
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<center><math>(1230)^\star B^+ (1213)^\star B^+ (1023)^\star B^+ = (1123)^\star B^+ (1203)^\star B^+ (1231)^\star B^+</math>.</center> |
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Thus the R3 component of <math>d</math> is |
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<center><math>(1230)^\star b^+ +(1213)^\star b^+ +(1023)^\star b^+ -(1123)^\star b^+ -(1203)^\star b^+ -(1231)^\star b^+</math>.</center> |
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===The Syzygies=== |
===The Syzygies=== |
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Revision as of 15:20, 18 November 2006
The Generators
Our generators are [math]\displaystyle{ T }[/math], [math]\displaystyle{ R }[/math], [math]\displaystyle{ Y=\Phi }[/math] and [math]\displaystyle{ B^{\pm} }[/math]. (You might consider splitting [math]\displaystyle{ Y }[/math] into two, [math]\displaystyle{ Y^{up} }[/math] and [math]\displaystyle{ Y^{dn} }[/math]). In pictures, they are
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| [math]\displaystyle{ T }[/math] | [math]\displaystyle{ R }[/math] | [math]\displaystyle{ Y^{up} }[/math] | [math]\displaystyle{ Y^{dn} }[/math] | [math]\displaystyle{ B^+ }[/math] | [math]\displaystyle{ B^- }[/math] |
The Relations
The Reidemeister Move R3
The picture is
In formulas, this is
Thus the R3 component of [math]\displaystyle{ d }[/math] is
