Knots of (canonical) genus two

Cited 20 time in webofscience Cited 0 time in scopus
  • Hit : 186
  • Download : 0
We give a description of all knot diagrams of canonical genus 2 and 3, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3- and 4-move conjectures, and the calculation of the maximal hyperbolic volume for canonical (weak) genus 2 knots. We also study the values of the link polynomials at roots of unity, extending denseness results of Jones. Using these values, examples of knots with non-sharp Morton (canonical genus) inequality are found. Several results axe generalized to arbitrary canonical genus.
Publisher
POLISH ACAD SCIENCES INST MATHEMATICS
Issue Date
2008
Language
English
Article Type
Article
Keywords

POLYNOMIAL INVARIANT; LINK POLYNOMIALS; JONES POLYNOMIALS; ALTERNATING KNOTS; POSITIVE KNOTS; 3-MANIFOLDS; FOLIATIONS; SIGNATURE; BRAIDS; NUMBER

Citation

FUNDAMENTA MATHEMATICAE, v.200, no.1, pp.1 - 67

ISSN
0016-2736
DOI
10.4064/fm200-1-1
URI
http://hdl.handle.net/10203/88965
Appears in Collection
RIMS Journal Papers
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 20 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0