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This article is about the mathematical concept. For the Unix system call, see unlink (Unix).
Unlink |
2-component unlink
|
Common name |
Circle |
Crossing no. |
0 |
Linking no. |
0 |
Stick no. |
6 |
Unknotting no. |
0 |
Conway notation |
- |
A-B notation |
02
1 |
Dowker notation |
- |
Next |
L2a1 |
Other |
, tricolorable (if n>1) |
|
Look up unlink in Wiktionary, the free dictionary. |
In the mathematical field of knot theory, the unlink is a link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane.
Contents
- 1 Properties
- 2 Examples
- 3 See also
- 4 Further reading
Properties
- An n-component link L ⊂ S3 is an unlink if and only if there exists n disjointly embedded discs Di ⊂ S3 such that L = ∪i∂Di.
- A link with one component is an unlink if and only if it is the unknot.
- The link group of an n-component unlink is the free group on n generators, and is used in classifying Brunnian links.
Examples
- The Hopf link is a simple example of a link with two components that is not an unlink.
- The Borromean rings form a link with three components that is not an unlink; however, any two of the rings considered on their own do form a two-component unlink.
- Kanenobu[who?] has shown that for all n > 1 there exists a hyperbolic link of n components such that any proper sublink is an unlink (a Brunnian link). The Whitehead link and Borromean rings are such examples for n = 2, 3.[full citation needed]
See also
Further reading
- Kawauchi, A. A Survey of Knot Theory. Birkhauser.
Knot theory (knots and links)
|
|
Hyperbolic |
- Figure-eight (41)
- Three-twist (52)
- Stevedore (61)
- 62
- 63
- Endless (74)
- Carrick mat (818)
- Perko pair (10161)
- (−2,3,7) pretzel (12n242)
- Whitehead (52
1)
- Borromean rings (63
2)
- L10a140
|
|
Satellite |
|
|
Torus |
- Unknot (01)
- Trefoil (31)
- Cinquefoil (51)
- Septafoil (71)
- Unlink (02
1)
- Hopf (22
1)
- Solomon's (42
1)
|
|
Invariants |
- Alternating
- Arf invariant
- Bridge no.
- Brunnian
- Chirality
- Crosscap no.
- Crossing no.
- Finite type invariant
- Hyperbolic volume
- Khovanov homology
- Genus
- Knot group
- Link group
- Linking no.
- Polynomial
- Alexander
- Bracket
- HOMFLY
- Jones
- Kauffman
- Pretzel
- Prime
- Stick no.
- Tricolorability
- Unknotting no. & problem
|
|
Notation &
operations |
- Alexander–Briggs notation
- Conway notation
- Dowker notation
- Flype
- Mutation
- Reidemeister move
- Skein relation
- Tabulation
|
|
Other |
- Alexander's theorem
- Berge
- Braid theory
- Conway sphere
- Complement
- Double torus
- Fibered
- Knot
- List of knots and links
- Ribbon
- Slice
- Sum
- Tait conjectures
- Twist
- Wild
- Writhe
|
|
|
UpToDate Contents
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English Journal
- Adaptive gene introgression after secondary contact.
- Uecker H1, Setter D, Hermisson J.
- Journal of mathematical biology.J Math Biol.2015 Jun;70(7):1523-80. doi: 10.1007/s00285-014-0802-y. Epub 2014 Jul 4.
- By hybridization and backcrossing, alleles can surmount species boundaries and be incorporated into the genome of a related species. This introgression of genes is of particular evolutionary relevance if it involves the transfer of adaptations between populations. However, any beneficial allele will
- PMID 24992884
- Microbial diversity. Fine-scale diversity and extensive recombination in a quasisexual bacterial population occupying a broad niche.
- Rosen MJ1, Davison M2, Bhaya D3, Fisher DS4.
- Science (New York, N.Y.).Science.2015 May 29;348(6238):1019-23. doi: 10.1126/science.aaa4456.
- Extensive fine-scale genetic diversity is found in many microbial species across varied environments, but for most, the evolutionary scenarios that generate the observed variation remain unclear. Deep sequencing of a thermophilic cyanobacterial population and analysis of the statistics of synonymous
- PMID 26023139
- Prevalence of HIV and syphilis infections among pregnant women attending antenatal clinics in Tanzania, 2011.
- Manyahi J1, Jullu BS2, Abuya MI3, Juma J4, Ndayongeje J5, Kilama B6, Sambu V7, Nondi J8, Rabiel B9, Somi G10, Matee MI11.
- BMC public health.BMC Public Health.2015 May 22;15:501. doi: 10.1186/s12889-015-1848-5.
- BACKGROUND: The occurrence of HIV-1 and syphilis infections during pregnancy poses major health risks to the foetus due to mother-to-child transmission. We conducted surveillance of HIV and syphilis infections among pregnant women attending antenatal clinics (ANCs) in Mainland Tanzania in 2011.METHO
- PMID 25994129
Japanese Journal
- Postoperative Results of Total Elbow Arthroplasty in Patients with Rheumatoid Arthritis Using the Unlinked J-alumina Ceramic Elbow Prosthesis
- Balb/c-congenic ANP32B-deficient mice reveal a modifying locus that determines viability
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