On the crossing number of semiadequate links
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Alexander Stoimenow
Abstract.
The concept of adequacy of a link was introduced to determine its crossing number. We give crossing number estimates for the (much larger) class of semiadequate links, in particular improving the previously known estimates for positive links. We also give examples showing that semiadequacy may not be attained in minimal crossing number diagrams. Our approach uses the description of links of a given canonical genus, and is related to skein invariants, the signature, the new concordance invariants, and hyperbolic volume. It allows to settle the A/B-adequacy status of many examples, including all knots up to 10 crossings. As two applications, we describe generic alternating and positive knots of given genus, determining the asymptotical behaviour of the number of such knots, and classify Seifert fibered, and therewith also hyperbolic, Montesinos links.
I would like to thank to D. Bar-Natan, N. Dunfield, M. Hirasawa, M. Kidwell, M. Ozawa and A. Vdovina for some helpful remarks. V. Goryunov helped me improving the style and exposition at many places.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Loop homology of spheres and complex projective spaces
- Symmetries of the positive semidefinite cone
- On the distribution of cubic exponential sums
- The tempered spectrum of quasi-split classical groups III: The odd orthogonal groups
- Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and q-zeta functions
- Multiplicative properties of Quinn spectra
- On the crossing number of semiadequate links
- “Spectral implies Tiling” for three intervals revisited
- Mock modular grids and Hecke relations for mock modular forms
Articles in the same Issue
- Frontmatter
- Loop homology of spheres and complex projective spaces
- Symmetries of the positive semidefinite cone
- On the distribution of cubic exponential sums
- The tempered spectrum of quasi-split classical groups III: The odd orthogonal groups
- Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and q-zeta functions
- Multiplicative properties of Quinn spectra
- On the crossing number of semiadequate links
- “Spectral implies Tiling” for three intervals revisited
- Mock modular grids and Hecke relations for mock modular forms
