Download e-book for iPad: Formal Knot Theory (Mathematical Notes, No. 30) by Louis H. Kauffman

By Louis H. Kauffman

ISBN-10: 048645052X

ISBN-13: 9780486450520

ISBN-10: 0691083363

ISBN-13: 9780691083360

The Description for this booklet, Formal Knot idea. (MN-30): , might be forthcoming.

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Additional info for Formal Knot Theory (Mathematical Notes, No. 30)

Example text

A G' Proof' of'~. D. J = lSH' Since J D = ltt' 0 it suff'ices to show that Since this property is preserved under applica t10n of' the interaction rules, the result follows by induetion. ~. It is worth observing how things go wrong when the interaction rules are violated. site to J(F') = --& in ~ DJ(Ff) ! F' (and DJ(F') - = -@-. ). Before proving Theorem placement ot atate ~'. the f'orm and F' For example, if we add a ma~ke~l. 17. we need a lemma about the Conlider an atomic string. 17. tring go to tbe right in tbe 'oro ~ where the + sign labels the cusp from the top part ot tbe shell.

The number of mi!! 1W.. t....!. There is good computational evidence for this conjecture. We shall compute one example at the end of the section. 3 we need an indexing of regions due to Alexander «(1]). Each region is assigned an integer index so that adjacent regions by one. hav~ indices differing The increase or decrease of index from region to region depends upon the orientation of the intervening boundary as in the schema below. ~ hl. 22!. pattern Every universe has an Alexander indeXing.

45 clockwise~, to', 2. Each exchange site marker rotates 3. For markers that move, those at sites between the midline and the top or bottom will turn a total ot 180· clockwise, while those markers at selfinteraction sites of the midline will turn a total of 360· clockwise. 4. If A is an atom in the decomposition of the midline, and it A has a cusp rider, then every marker on A will turn. 5. Call an atom involved it all of its markers turn in the tactorization. It A is involved, and A < B, then B is involved.

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Formal Knot Theory (Mathematical Notes, No. 30) by Louis H. Kauffman


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