查看“︁亞歷山大多項式”︁的源代码

在[[紐結理論|纽结理论]]中，'''亚历山大多项式（Alexander polynomial）'''是一种[[紐結多項式]]。<ref>Alexander describes his skein relation toward the end of his paper under the heading "miscellaneous theorems", which is possibly why it got lost. [[Joan Birman]] mentions in her paper ''New points of view in knot theory'' (Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 253–287) that Mark Kidwell brought her attention to Alexander's relation in 1970.</ref>

== 亚历山大–康威多项式 ==
[[File:Skein_(HOMFLY).svg|居中|200x200像素]]

* <math>\nabla(O) = 1</math> (unknot)
* <math>\nabla(L_+) - \nabla(L_-) = z \nabla(L_0)</math>

<math>\Delta_L(t^2) = \nabla_L(t - t^{-1})</math>

<math>\Delta(L_+) - \Delta(L_-) = (t^{1/2} - t^{-1/2}) \Delta(L_0)</math>

== 参考文献 ==
{{Reflist}}

== 阅读 ==

* {{Cite journal|title=Topological invariants of knots and links|last=Alexander|first=J. W.|authorlink=James Waddell Alexander II|journal=[[Transactions of the American Mathematical Society]]|issue=2|doi=10.2307/1989123|year=1928|volume=30|pages=275–306|jstor=1989123}}
* {{Cite book|first=Richard|last=Crowell|first2=Ralph|last2=Fox|authorlink2=Ralph Fox|title=Introduction to Knot Theory|url=https://archive.org/details/introductiontokn0000crow|publisher=Ginn and Co. after 1977 Springer Verlag|year=1963|ref=harv}}
* {{Cite book|first=Colin C.|last=Adams|authorlink=Colin Adams (mathematician)|title=The Knot Book: An elementary introduction to the mathematical theory of knots|edition=Revised reprint of the 1994 original|publisher=American Mathematical Society|location=Providence, RI|year=2004|isbn=978-0-8218-3678-1}} (accessible introduction utilizing a skein relation approach)
* {{Cite journal|title=A quick trip through knot theory, In Topology of ThreeManifold|last=Fox|first=Ralph|authorlink=Ralph Fox|publisher=Prentice-Hall|year=1961|location=Englewood Cliffs. N. J.|edition=Proceedings of 1961 Topology Institute at Univ. of Georgia, edited by M.K.Fort|pages=120–167|ref=harv}}
* {{Cite book|authorlink=Michael H. Freedman|first=Michael H.|last=Freedman|authorlink2=Frank Quinn (mathematician)|first2=Frank|last2=Quinn|title=Topology of 4-manifolds|series=Princeton Mathematical Series|volume=39|publisher=Princeton University Press|location=Princeton, NJ|year=1990|isbn=978-0-691-08577-7|url=https://archive.org/details/topologyof4manif0000free}}
* {{Cite journal|title=Formal Knot Theory|url=https://archive.org/details/formalknottheory0000kauf|last=Kauffman|first=Louis|authorlink=Louis Kauffman|publisher=[[Princeton University Press]]|year=1983|ref=harv}}
* {{Cite book|first=Louis|last=Kauffman|authorlink=Louis Kauffman|title=Knots and Physics|publisher=World Scientific Publishing Company|year=2012|edition=4th|ref=harv|isbn=978-981-4383-00-4}}
* {{Cite book|first=Akio|last=Kawauchi|title=A Survey of Knot Theory|publisher=Birkhauser|year=1996|isbn=}} (covers several different approaches, explains relations between different versions of the Alexander polynomial)
* {{Cite journal|title=Holomorphic disks and knot invariants|last=Ozsváth|first=Peter|last2=Szabó|first2=Zoltán|authorlink2=Zoltán Szabó (mathematician)|journal=[[Advances in Mathematics]]|issue=1|doi=10.1016/j.aim.2003.05.001|year=2004|volume=186|pages=58–116|arxiv=math/0209056|bibcode=2002math......9056O|ref=harv}}
* {{Cite journal|title=Holomorphic disks and genus bounds|last=|first=Peter|last2=Szabó|first2=Zoltán|authorlink2=Zoltán Szabó (mathematician)|journal=[[Geometry and Topology]]|issue=2004|doi=10.2140/gt.2004.8.311|year=2004b|volume=8|pages=311–334|arxiv=math/0311496|ref=harv}}
* {{Cite journal|title=Knot Floer homology detects fibred knots|url=https://archive.org/details/sim_inventiones-mathematicae_2007_170_3/page/577|last=Ni|first=Yi|journal=Inventiones Mathematicae|issue=3|doi=10.1007/s00222-007-0075-9|year=2007|series=Invent. Math.|volume=170|pages=577–608|arxiv=math/0607156|bibcode=2007InMat.170..577N|ref=harv}}
* {{Cite thesis|first=Jacob|last=Rasmussen}}
* {{Cite book|first=Dale|last=Rolfsen|authorlink=Dale Rolfsen|title=Knots and Links|edition=2nd|location=Berkeley, CA|publisher=Publish or Perish|year=1990|isbn=978-0-914098-16-4}} (explains classical approach using the Alexander invariant; knot and link table with Alexander polynomials)

== 外部链接 ==
* {{Springer|title=Alexander invariants|id=p/a011300}}
* "Main Page" and "The Alexander-Conway Polynomial", The Knot Atlas.&nbsp;– knot and link tables with computed Alexander and Conway polynomials

{{纽结理论}}
[[Category:多項式]]
[[Category:紐結理論]]