Abstract
A natural generalization of a crossing change is a rational subtangle replacement (RSR). We characterize the fundamental situation of the rational tangles obtained from a given rational tangle via RSR, building on work of Berge and Gabai, and determine the sites where these RSR may occur. In addition we also determine the sites for RSR distance at least two between 2-bridge links. These proofs depend on the geometry of the branched double cover. Furthermore, we classify all knots in lens spaces whose exteriors are generalized Seifert fibered spaces and their lens space surgeries, extending work of Darcy and Sumners. This work is in part motivated by the common biological situation of proteins cutting, rearranging and resealing DNA segments, effectively performing RSR on DNA "tangles".
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1413-1463 |
| Number of pages | 51 |
| Journal | Algebraic and Geometric Topology |
| Volume | 13 |
| Issue number | 3 |
| DOIs | |
| State | Published - Apr 30 2013 |
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Keywords
- Branched cover
- Rational tangle
- Tangle replacement
ASJC Scopus subject areas
- Geometry and Topology
Cite this
The classification of rational subtangle replacements between rational tangles. / Baker, Kenneth; Buck, Dorothy.
In: Algebraic and Geometric Topology, Vol. 13, No. 3, 30.04.2013, p. 1413-1463.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The classification of rational subtangle replacements between rational tangles
AU - Baker, Kenneth
AU - Buck, Dorothy
PY - 2013/4/30
Y1 - 2013/4/30
N2 - A natural generalization of a crossing change is a rational subtangle replacement (RSR). We characterize the fundamental situation of the rational tangles obtained from a given rational tangle via RSR, building on work of Berge and Gabai, and determine the sites where these RSR may occur. In addition we also determine the sites for RSR distance at least two between 2-bridge links. These proofs depend on the geometry of the branched double cover. Furthermore, we classify all knots in lens spaces whose exteriors are generalized Seifert fibered spaces and their lens space surgeries, extending work of Darcy and Sumners. This work is in part motivated by the common biological situation of proteins cutting, rearranging and resealing DNA segments, effectively performing RSR on DNA "tangles".
AB - A natural generalization of a crossing change is a rational subtangle replacement (RSR). We characterize the fundamental situation of the rational tangles obtained from a given rational tangle via RSR, building on work of Berge and Gabai, and determine the sites where these RSR may occur. In addition we also determine the sites for RSR distance at least two between 2-bridge links. These proofs depend on the geometry of the branched double cover. Furthermore, we classify all knots in lens spaces whose exteriors are generalized Seifert fibered spaces and their lens space surgeries, extending work of Darcy and Sumners. This work is in part motivated by the common biological situation of proteins cutting, rearranging and resealing DNA segments, effectively performing RSR on DNA "tangles".
KW - Branched cover
KW - Rational tangle
KW - Tangle replacement
UR - http://www.scopus.com/inward/record.url?scp=84877094062&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84877094062&partnerID=8YFLogxK
U2 - 10.2140/agt.2013.13.1413
DO - 10.2140/agt.2013.13.1413
M3 - Article
AN - SCOPUS:84877094062
VL - 13
SP - 1413
EP - 1463
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 3
ER -