56 lines
2.3 KiB
BibTeX
56 lines
2.3 KiB
BibTeX
@article{Kauffman1990-qe,
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title = {An invariant of regular isotopy},
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author = {Kauffman, Louis H},
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abstract = {This paper studies a two-variable Laurent polynomial invariant
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of regular isotopy for classical unoriented knots and links.
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This invariant is denoted L K \{L\_K\} for a link K K , and it
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satisfies the axioms: 1. Regularly isotopic links receive the
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same polynomial. 2. L [ unk ] = 1 \{L\_\{[\{\textbackslashtext
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\{unk\}\}]\}\} = 1 . 3. L [ unk ] = a L , L [ unk ] = a − 1 L
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\{L\_\{[\{\textbackslashtext \{unk\}\}]\}\} =
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aL,\textbackslashqquad \{L\_\{[\{\textbackslashtext
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\{unk\}\}]\}\} = \{a^\{ - 1\}\}L . 4. L [ unk ] + L [ unk] = z (
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L [ unk] + L [ unk] ) \{L\_\{[\{\textbackslashtext
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\{unk\}\}]\}\} + \{L\_\{[\{\textbackslashtext \{unk]\}\}\}\} =
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z(\{L\_\{[\{\textbackslashtext \{unk]\}\}\}\} +
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\{L\_\{[\{\textbackslashtext \{unk]\}\}\}\}) . Small diagrams
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indicate otherwise identical parts of larger diagrams. Regular
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isotopy is the equivalence relation generated by the
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Reidemeister moves of type II and type III. Invariants of
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ambient isotopy are obtained from L L by writhe-normalization.},
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journal = {Trans. Am. Math. Soc.},
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publisher = {American Mathematical Society (AMS)},
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volume = 318,
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number = 2,
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pages = {417--471},
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year = 1990,
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language = {en}
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}
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@online{wiki:wild_knot,
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author = {Jkasd},
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title = {Wild knot.svg},
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year = {2008},
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url = {https://commons.wikimedia.org/wiki/File:Wild_knot.svg},
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note = {Public domain, via Wikimedia Commons}
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}
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@book{crowell1977introduction,
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title = {Introduction to Knot Theory},
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author = {Crowell, R.H. and Fox, R.H.},
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isbn = {9783540902720},
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lccn = {77022776},
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series = {Graduate Text in Mathematics},
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year = {1977},
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publisher = {Springer New York}
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}
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@book{lickorish1997introduction,
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title = {An Introduction to Knot Theory},
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author = {Lickorish, W.B.R.},
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isbn = {9780387982540},
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lccn = {97016660},
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series = {Graduate Texts in Mathematics},
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year = {1997},
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publisher = {Springer New York}
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} |